WASHINGTON—The Federal Reserve plans to hit the biggest U.S. banks with a costly new requirement aimed at reducing the risk that some financial firms remain "too big to fail" nearly six years after the financial crisis erupted.

In testimony prepared for a Senate Banking Committee hearing Tuesday, Fed Governor Daniel Tarullo said the regulator intends to impose a capital surcharge that will require the biggest U.S. banks to maintain fatter cushions to protect against potential losses. The Fed's version of the capital...