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  Proskauer Rose LLP    1001 Pennsylvania Avenue, NW Suite 600 South    Washington, DC 20004-2533

June 16, 2023

VIA EDGAR

David Manion

Senior Staff Accountant

Division of Investment Management

U.S. Securities and Exchange Commission

100 F Street, N.E.

Washington, D.C. 20549

Re:         IDR Core Property Index Fund Ltd

Annual Report on Form N-CSR

For the Fiscal Year ended June 30, 2022 (File
No. 811-23460)

Dear Mr. Manion:

On behalf of IDR Core Property Index Fund Ltd
(the “Fund”), set forth below are the Fund’s responses to the oral comments provided by the staff
of the Division of Investment Management (the “Staff”) of the Securities and Exchange Commission (the “Commission”)
to the Fund on June 8, 2023, with respect to the Fund’s Annual Report on Form N-CSR (File No. 811-23460), filed with the Commission
on September 7, 2022, and the financial statements included therein (the “Financial Statements”), and the Fund’s
related Annual Report on Form N-CEN (File No. 811-23460), filed with the Commission on September 9, 2022. The Staff’s comments are
set forth below in italics and are followed by the Fund’s responses.

 1. Comment: The Fund's Statement of Assets and Liabilities identifies a receivable from its investment
adviser, IDR Investment Management, LLC (the “Manager”), in the amount of $1,264,125 (the "Receivable").
With respect to the Receivable, please discuss in your response the following: (i) the nature of the amount indicated in the Receivable;
(ii) whether amounts due to the Fund have been remitted and when the amounts were paid; (iii) the accounting policies related to the timing
and remittance of management fees and the amounts that due to the Manager; (iv) whether all expenses of the Fund are current as of June
30, 2022; and (v) whether the Manager is able to meet its payment obligations of the Fund.

Response: The Fund advises the
Staff on a supplemental basis that the amounts underlying the Receivable directly related to certain expenses that had accrued but had
not yet been paid by the Fund to third party service providers for services rendered to it. The Manager will generally either pay such
expenses directly on behalf of the Fund, or alternatively reimburse the Fund when such expenses are paid by it. Because the third-party
expenses underlying the Receivable had not yet been paid either by the Fund or the Manager as of June 30, 2022, the Manager remained subject
to a payment obligation to the Fund in the amount of such third-party expenses, which obligation was reflected in the Receivable. The
Fund confirms that any reduction in the amount of the Receivable reflects either the assumption of such third-party expense by the Manager
or the reimbursement of a third-party expense paid by the Fund and reimbursed by the Manager. To the extent the Fund paid any third-party
expenses underlying the Receivable, such amounts were promptly reimbursed by the Manager. Notably, the aggregate amount of such Receivable
had been reduced to $0 as of March 31, 2023. Finally, the Fund advises the Staff on a supplemental basis that the Manager presently manages
private funds with an investment strategy similar to that of the Fund which have approximately
$5.4 billion in total assets as of March 31, 2023. Accordingly, the Fund believes the Manager has sufficient cash flow and income from
operations to meet its payment obligations to the Fund.

Beijing | Boca Raton | Boston | Chicago | Hong
Kong | London | Los Angeles | New Orleans | New York | Paris | São Paulo | Washington, DC

 2. Comment: In the Fund’s Annual Report on Form N-CEN for the fiscal year ended June 30,
2022, the Fund disclosed in Item D.8. that the management fee as a percentage of net assets was 0.30%, which included a 0.10% fee waiver
as of such date. In future filings, please report the Fund’s contractual advisory fee as of the end of the reporting period as a
percentage of net assets, without regard to any waiver or expense limit.

Response: The Fund acknowledges
the Staff’s comment and confirms that it will revise the above-referenced disclosure in future filings.

 3. Comment: In connection with the Fund's organizational and offering expenses incurred by the
Manager as discussed in Note 4 to the Fund's Financial Statements, amounts reimbursable by the Fund are identified through June 30, 2027.
Please discuss in correspondence why no liability has been recorded for these reimbursable amounts or how these reimbursable amounts are
recorded. The discussion should include whether the reimbursable amounts, as of June 30, 2022, are included in the Statement of Assets
and Liabilities as a payable to the Manager or any other third party. Please include in the discussion any references to ASC 450, ASC
946-20-05-8, and any other relevant accounting guidance.

Response: The Fund advises the
Staff on a supplemental basis that notwithstanding the payment of its organizational and offering expenses (“O&O Expenses”)
by the Manager on its behalf, it nonetheless opted to amortize such O&O Expenses over the twelve-month period following the commencement
of operations on April 1, 2021. Accordingly, the Fund included specific line items on its Income Statement for the period from April 1,
2021 through June 30, 2021 for both organizational expenses and offering expenses, and included a similar line item for offering expenses
on its Income Statement for the fiscal year ended June 30, 2022. As of June 30, 2022, however, the Fund did not believe that it would
be appropriate to accrue a liability for reimbursement of the O&O Expenses paid by the Manager on Fund’s behalf as it did not
believe that such reimbursements were either probable or reasonably estimable.

Specifically, ASC 450-20-25-2 requires
that a liability be accrued if (i) information available before the financial statements are issued indicates that it is probable that
a liability has been incurred as of the date of the financial statements, and (ii) the amount of such liability is reasonably estimated.
In addition, ASC 946-20-05-8 recognizes that certain unreimbursed expenses may be carried over and reimbursed in a future period when
and if certain criteria are met, subject to a maximum reimbursement period. ASC 946-20-25-4 in turn requires that the criteria set forth
in ASC 450-20-25-2 be met before a liability is accrued with respect to such excess unreimbursed expenses. Notably, as of June 30, 2022,
and through the date the Financial Statements were available to be issued, the Fund did not believe that it was probable that it would
be required to reimburse the Manager for material additional O&O Expenses incurred on the Fund’s behalf pursuant to the Organizational
and Offering Expense Limitation Agreement to which the Fund and the Manager are a party (the “O&O ELA”).

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Specifically, the Fund had raised
only approximately $23.6 million in new capital from investors as of June 30, 2022 (excluding reinvestment of dividends), despite
marketing the Fund’s shares for a period of over 15 months. As a result, based on the terms of the O&O ELA, the Manager
was only entitled to approximately $118,000, or 0.50% of the gross proceeds raised, as of June 30, 2022. Even that amount of
reimbursement, however, was ultimately waived by the Manager. The Fund has unfortunately struggled with raising additional capital
since its initial launch, and notably has raised only $9.5 million in additional capital to date during its fiscal year ending June
30, 2023. Such struggles form the basis for its proposed restructuring referenced in its recent Registration Statement on Form N-2
and related proxy materials on Schedule 14A (the “Proposed Restructuring”). The Fund notes that even if
the reimbursement of a further portion of such O&O Expenses was probable, it believes that the amount thereof could not be
reasonably estimated in view of the significant difficulty the Fund had experienced in its fund-raising efforts through June 30,
2022. Based on the Fund’s capital raising history and difficulties encountered since its inception, as of June 30, 2022, not
only was it not probable that a reimbursement would occur, but it seemed unlikely that the Fund would be able to raise enough new
capital to cause any of the waived O&O Expenses to be reimbursed at all per the terms of the O&O ELA.

The Fund further notes that in the open-end
fund context, the AICPA Financial Reporting Executive Committee (FinREC) has observed that even actual reimbursement of some fund expenses
does not necessarily establish the appropriateness of accrual of additional unreimbursed amounts if future conditions must be met to permit
reimbursement to occur.  While not directly on point, the Fund believes the FinREC view is analogous to the Fund’s circumstances,
where significant uncertainty remains with respect to the Fund’s ability to raise material additional capital from investors, the
absence of which would preclude further reimbursement of any additional O&O Expenses.

If you have any questions or additional comments
concerning the foregoing, please contact William MacGregor by phone at 212.969.3555 or by email at wmacgregor@proskauer.com, or
the undersigned by phone at 202.416.6828 or by email at jmahon@proskauer.com.

  Sincerely,

  /s/ John J. Mahon

  John J. Mahon, Esq.

cc:          Gary A. Zdolshek, Chief Executive Officer and President

Thomas Bartos, Chief Financial Officer

William MacGregor, Esq.

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