The team was founded as Leavine Fenton Racing by Bob Leavine and Lance Fenton in early 2011, making its Cup Series debut at Texas Motor Speedway in April of that year with David Starr driving. Fenton departed shortly after and his share was acquired by the Leavines, who renamed the organisation Leavine Family Racing. The number 95 was chosen as a tribute to Lightning McQueen from the Pixar film Cars. Starr's best finish in 2011 was a 27th place at Bristol Motor Speedway.
For 2012, the team hired former Formula 1 and Champ Car driver Scott Speed to drive a planned fifteen-race schedule. Speed achieved a ninth-place finish at the 2013 Aaron's 499 — the team's best result at that stage — but grew frustrated with the team's start-and-park approach to many events and departed after the Atlanta race in 2013.
Michael McDowell joined the team for 2014, bringing KLOVE and Thrivent Financial sponsorship that enabled a genuine race-distance programme for the first time. The team entered an alliance with Team Penske, gaining technical support and improved equipment. At the 2014 Coke Zero 400 at Daytona, McDowell and the team achieved a career-best seventh-place finish in a rain-shortened event.
McDowell returned for 2015 and the team maintained its Penske alliance through continued K-LOVE and Thrivent backing. The team's shop partially burned down during the summer of 2015, forcing temporary operations from Team Penske's campus until repairs were made. In January 2016 longtime NASCAR team owner Joe Falk became an investor, merging his Circle Sport operation with the team — known temporarily as Circle Sport-Leavine Family Racing — and bringing a charter that guaranteed the No. 95 its first full season of racing. The team switched to Chevrolet and allied with Richard Childress Racing. Falk departed at the end of 2016 and his charter left with him, prompting Leavine to purchase a replacement charter from Tommy Baldwin Racing.
Former Hendrick Motorsports driver Kasey Kahne replaced McDowell for the 2018 season. Kahne's tenure was disrupted by heat exhaustion at the Southern 500 and subsequent health complications that caused him to miss the final portion of the season. Regan Smith substituted in the car during Kahne's absence. Kahne announced the end of his full-time racing career at the conclusion of 2018.
Matt DiBenedetto signed a two-year contract to drive the No. 95 starting in 2019, and the team switched from Chevrolet to Toyota while entering a technical alliance with Joe Gibbs Racing. DiBenedetto delivered the team's strongest sustained performances, leading 49 laps in the 2019 Daytona 500 before being collected in a late incident. He scored a career-high fourth at Sonoma and, most notably, finished second at the Bristol Night Race — the highest finish in Leavine Family Racing's history. DiBenedetto's 2019 season established him as a driver of genuine Cup Series potential.
Christopher Bell, fresh off a NASCAR Xfinity Series championship with JGR's programme, was announced as the 2020 driver on September 24, 2019. The team completed its final season with Bell in the No. 95, finishing twentieth in points.
In July 2020, Bob Leavine confirmed he had solicited bids for the team due to the financial impact of the COVID-19 pandemic. The team's assets were sold, with its fleet of Toyota cars returning to Joe Gibbs Racing and the broader asset base acquired by Spire Motorsports. The final race was run at the end of the 2020 season.
Leavine Family Racing's decade-long Cup Series run illustrated the challenges and occasional breakthroughs available to well-intentioned independent operations. The team's progression from start-and-park outings to a legitimate JGR technical alliance and near-race-winning pace with DiBenedetto represented meaningful competitive development. The Bristol second-place finish in 2019 remains the team's most competitive result and DiBenedetto's best Cup result to that point.