During World War II he commanded the U-Boote Medusa and Barbarigo. He claimed that on May 20, 1942 he attacked and sank a Maryland-class USN battleship. He also believed that he surface attacked and sank a Mississippi-class USN battleship on October 6, 1942. Both of these attacks were proved to be unsuccessful and Mussolini's order to promote Grossi to Capitano di Fregata and the prestigious award of Medaglia d'oro al valor militare was premature. (Luigi Rizzo, a World War I naval hero was honred with the same highly prestigious award, who sank the Austro-Hungarian battleship Szent Istvan).