Born in Las Palmas, Gran Canaria to a Swedish father and an English mother, Suneson represented England in amateur competition and attended Oklahoma State University in the USA. Carl opted to take Spanish citizenship in 1996.
Suneson turned professional in 1989 and played extensively on the European Tour and European Challenge Tour. He had to wait 18 years, his 256th start before claiming his first title on the DP World Tour – the 2007 Open de Saint-Omer. He has won six times on the European Challenge Tour, placing him tied third in the all-time winners list standings.
| Best Legends Tour Finish | 6 |
| Professional Wins | 6 |
| Turned Pro | 1989 |
