Greg Beck launched the team in 1995 to field entries in the newly formed Indy Racing League, siding with the IRL during the CART–IRL split of 1996. The team operated at varying levels of commitment across fifteen years, ranging from full-season campaigns to one-off Indianapolis 500 entries. Throughout its existence Beck Motorsports built partnerships with prominent motorsport figures including promoter Cary Agajanian and music executive Mike Curb of Curb Records.
The team made its debut at the 1995 Indianapolis 500 with Japanese driver Hideshi Matsuda, who finished 15th. When the IRL launched as a standalone series in 1996, Beck committed to a full-time programme with Robbie Buhl, who finished third in the series' inaugural race at Walt Disney World Speedway and ended the year third in the championship standings. Matsuda also returned for the 1996 Indy 500, achieving a career-best eighth-place finish.
Buhl departed after the start of the 1996–97 season to join the better-resourced Team Menard, leaving Beck to field Dennis Vitolo solely at the Indianapolis 500 in 1997. The team struggled badly with underpowered Infiniti engines and relied on the so-called "25 and 8 rule" — a guaranteed starting position based on prior season points — to make the field; Vitolo finished 15th. Beck did not return for 1998.
The team re-appeared for one-off Indy 500 efforts in 1999 and 2000 with Matsuda. In 1999 he qualified and finished 10th; in 2000 he failed to qualify.
For 2001, Beck joined forces with the Curb Agajanian Performance Group and returned to full-time racing with veteran driver Billy Boat. Boat delivered a strong result with a second-place finish at Nashville Superspeedway and concluded the season fourth in the championship standings, representing one of the team's best competitive campaigns.
In 2002, Beck fielded a car in three mid-season races for Robby McGehee, plus Indy 500 entries for Japanese former Formula One driver Shinji Nakano (who finished 14th) and former F1 driver Johnny Herbert. Herbert failed to get his car in the qualifying line before the deadline on Pole Day and was subsequently replaced by Memo Gidley for the second qualifying weekend, though the entry was ultimately withdrawn.
The full CURB/Agajanian/Beck Motorsports partnership was formalised in 2004, fielding P.J. Jones at Indianapolis where he finished 28th. In 2005 the team ran a late entry for rookie Arie Luyendyk Jr., though handling problems prevented him from posting a competitive speed and the car was bumped from the field by Felipe Giaffone — the only entry eliminated during bumping that year.
For the 2006 Indianapolis 500, Beck merged temporarily with Team Leader Motorsports to field two cars: Jones for Beck's side and Stephan Gregoire for Kent Baker's side, with Curb Agajanian Motorsports backing both. The partnership dissolved after 2006, with Jones returning to Team Leader Motorsports for 2007.
Beck Motorsports made a surprise entry into the 2007 XM Satellite Radio Indy 300 at Homestead-Miami Speedway with Alex Barron, who also raced at Kansas Speedway and finished 15th at the Indy 500, one lap down.
In 2008, Roger Yasukawa drove the team's entry at Twin Ring Motegi and attempted to qualify at Indianapolis but was bumped from the field.
For 2009, the team rebranded as CURB/Agajanian/3G Racing — "3G" standing for Three Guys Racing — following the arrival of NASCAR driver Stanton Barrett and sports marketer Steve Sudler as partners. The season involved multiple driver changes: Barrett started the year before being replaced at Texas by Jaques Lazier, who covered oval events, while Richard Antinucci handled the road and street course rounds. Barrett returned to drive at Twin Ring Motegi, where he held personal sponsorship.
The team did not announce plans for 2010, though Sudler indicated hopes of securing sponsorship for Antinucci full-time and Barrett part-time. No entries materialised and the team did not appear at any 2010 races, effectively ending its competitive activity.
Beck Motorsports exemplified the small-team ecosystem that populated the early Indy Racing League, providing Indianapolis 500 opportunities for international drivers — particularly from Japan — and veteran oval specialists at a time when the series was establishing itself separately from CART. The team's willingness to field Japanese competitors including Matsuda, Nakano, and Yasukawa reflected the IRL's efforts to build connections with Japanese automotive partners during the Infiniti and Honda engine programmes.