Graziani signed with the Los Angeles Avengers prior to the 2001 season. He completed 23 out of 37 passes that season for 262 yards, seven touchdowns and one interception. He became the starter in 2002 as he completed 282 out of 467 passes for 3,568 yards, 67 touchdowns, and 1 interception. In 2003, he completed 304 of 495 passes for 4,290 yards, 96 touchdowns, and 15 interceptions. In 2004, he had his finest season as he completed 333 of 510 passes for 4,265 yards, 99 touchdowns, and five interceptions.