The estate of a real-estate heiress swindled by Bernie Madoff is trying to recoup $7.4 million from the IRS, claiming the Ponzi schemer filed a false tax return for the woman to keep his scam secret.

Gladys C. Luria, whose father, Henry Claman, built the Times Square Hotel in 1922, was supposedly worth $32 million when she died in 2005 at age 96, according to tax returns filed by Madoff, who is now serving a 150-year sentence for fraud.

But those tax returns were bogus, because Madoff had cheated Luria, along with thousands of others, in a historic Ponzi scheme, according to a Manhattan federal lawsuit filed against the US government by Luria’s estate.

“The value of the accounts at the date of [her] death was in fact zero, because the accounts had no securities in them . . . Madoff . . . knowingly filed a false return to cover up his criminal Ponzi scheme,” according to court papers.

Madoff’s crimes didn’t come to light until his arrest in 2008.

Luria was a Madoff client for so long she made Bernie and his brother, Peter, co-executors of her estate.

The family paid $10 million in estate taxes upon Luria’s death based upon the false return, an overpayment of $7.4 million, the estate alleges in its legal filing.

The IRS declined to comment.