Belmont began racing at an early age before relocating south to pursue professional competition. In 1987 he broke through in the NASCAR Dash Series, winning at Hickory Motor Speedway on October 18 and earning the Rookie of the Year title. The following season he posted two more victories — at Myrtle Beach Speedway on May 20, 1988, and Southside Speedway on July 8, 1988 — and his car owner's entry claimed the series championship. The NASCAR Dash Series has since evolved into the ISCARS DASH Touring series as of 2005.
Belmont made his Winston Cup debut in 1989 at Dover Downs International Speedway during the Peak Performance 500, starting 35th and finishing 29th after his No. 04 Winner Ford Cherry Hill Ford Thunderbird suffered braking failure. Despite running only eight races in 1992, he finished runner-up for the Winston Cup Rookie of the Year award, a remarkable result given the limited schedule. His best NASCAR finish came in the Busch Series in 1995 at Darlington Raceway. In 2006 Belmont attempted Cup racing again, entering a car in the Daytona 500 sponsored by Year One Muscle Cars and Fanscrew.com.
Belmont found his most sustained success at the ARCA Re/MAX Series level. Running just five ARCA events in 1995, he nevertheless earned three top-five finishes. Three years later he became a regular competitor, finishing fifth in the final 1998 point standings. He backed that up with a sixth-place result in 1999, then another top-ten finish the following season, giving him four consecutive years inside the ARCA top ten in points. Over 174 races in the ARCA Re/MAX Series Belmont did not win, but he accumulated 54 top-ten finishes, demonstrating consistent competitiveness across a lengthy span.
After stepping back from full-time driving, Belmont transitioned into team ownership. Andy Belmont Racing was based in Lexington, North Carolina, and fielded two cars weekly in the ARCA Racing Series presented by Re/Max and Menards. Driver Chad McCumbee became the team's most successful representative, winning two races for the organization in 2007 — at Nashville Superspeedway and Pocono Raceway — in only five starts. McCumbee also won the 2011 Allen Crowe 100 at Springfield and claimed the Bill France Four Crown title that season with ModSpace sponsorship while driving the No. 1 for Andy Belmont Racing. Mikey Kile was the team's final ARCA driver in 2012.
Belmont sold the race team in 2012 and returned to the Philadelphia area to assist with a family business. He has five children, two of whom work alongside him in the business on a daily basis.