Albright was the first woman to become Secretary of State when former President Bill Clinton appointed her in 1997. She also served on former President Jimmy Carter's National Security Council.
In a news release, Albright called Grimes one of the brightest young leaders in America.
Grimes is challenging Republican Sen. Mitch McConnell in one of the country's most-watched races as Republicans and Democrats battle for control of the Senate.
McConnell also has the support of a former secretary of state in Condoleezza Rice. The former Secretary of State under President George W. Bush headlined a fundraiser for McConnell at Rupp Arena in March in advance of the May 20 Republican primary.
