Palmer began his motorsport career in 2005 in the T -Cars - series in which racers aged 14 to 17 sedans were on the road, and was fifth in the autumn championship. In 2006 he started again in T Cars and finished fifth in the championship. After 2007, two T -Cars race that he decided both for himself participated, he moved to Formula racing and raced in the Formula Palmer Audi, a racing series which was founded by his father Jonathan Palmer. Jolyon Palmer won two races, finishing tenth overall. In 2008, he remained in the Formula Palmer Audi and improved, although he won only one race, the third overall.
2009 Palmer moved to the newly established FIA Formula 2 Championship, which was also organized by his father. The racers took three points and finished 21st overall. He also competed in eight races of the Formula Palmer Audi and was with a win 16th in the overall standings. 2010 Palmer remained in Formula 2 with a win in the opening race at Silverstone Palmer started the season well. He showed another impressive performance at Monza, where he won both races starting from pole position. After leading the championship for a long time, he was at the end of the season with a total of five wins runner-up behind Dean Stoneman.
2011 Palmer moved to Arden International, and stood in for the team in the GP2 Asia Series and GP2 Series. In the GP2 Asia Series, he finished the season 19th overall. In GP2 Palmer had no points and was 28th in the driver standings. After the season, he took part for the Barwa Addax team at the GP2 Final in 2011. With a third place as best result he was on the fourth place in the standings. In addition, he returned for a race weekend in Formula 2. The race, however, he did not start. For GP2 Series 2012 season changed Palmer within the GP2 Series for iSport International. In the second race weekend in as- Sachir he scored with a seventh place in the Sprint race first points in GP2 series. After his car stopped in the sprint race of the fourth race weekend before the start due to technical problems, the team to provide him the next event a new vehicle decided. With the new car, he managed the sprint race to decide for themselves right away in Monte Carlo. It was his first GP2 victory. With three podium finishes Palmer finished the season in eleventh place overall and thus was subject to his teammate Marcus Ericsson.
2013 Palmer received a GP2 cockpit at Carlin. At the Hungaroring, he scored his first GP2 main race win. This result he repeated in Singapore, where he succeeded, starting from pole position to achieve another victory in the feature race. Although his team-mate Felipe Nasr, unlike him, did not win a race, he sits down with 154 to 119 points within the team against Palmer by. Palmer finished seventh in the drivers' standings. 2014 Palmer moved within the GP2 Series for DAMS. The first race weekend in as- Sachir Palmer scored after a third place in the feature race victory in the sprint race. He led the drivers' championship to after the first race.
- 2005: T -Cars - Autumn Championship ( 5th place)
- 2006: Cars ( 5th place)
- 2007: Cars ( No. 11 )
- 2007: Formula Palmer Audi ( # 10 )
- 2008: Formula Palmer Audi ( 3rd place)
- 2008: Formula Palmer Audi Autumn series ( 3rd place)
- 2009: Formula 2 ( No. 21 )
- 2009: Formula Palmer Audi ( 16th place)
- 2010: Formula 2 (2nd place)
- 2011: GP2 Asia Series ( No. 19 )
- 2011: GP2 Series ( No. 28 )
- 2012: GP2 Series (No. 11)
- 2013: GP2 Series (No. 7)
- 2014: GP2 Series