A construction firm with a history of defrauding the federal government was awarded a $56 million contract by the MTA yesterday.

Schiavone Construction Co. landed the contract along with partner John P. Picone, Inc., to provide ventilation for planned train tunnels in Grand Central Terminal.

In 2010, Schiavone was forced to shell out $20 million in fines for defrauding the government by claiming to have hired minority- and women-owned businesses for some federally funded projects, when in fact, it hadn’t.

But MTA officials yesterday dismissed any concerns about using Schiavone for the new project.