He started his career at Faroese club GÍ Gøta, after a successful season in 2000, in which he scored 13 league goals, moved to Dutch side FC Zwolle in 2001, becoming the second Faroese international to play in the Netherlands after Jan Allan Müller played for Go Ahead Eagles in 1990/1991.

He returned to GÍ in 2002, and after a prolific number of goals for a midfielder, he attracted the attention of Danish team AaB, where he was later joined by Faroese teammate Jón Rói Jacobsen.

Olsen made his debut for the Faroe Islands national football team in January 2001, in a Nordic Championship match against Sweden, coming on as a substitute for Sámal Joensen.

He played magnificently against Estonia in a friendly in Summer 2008, scoring one goal and making two assists, bringing the Faroe Islands level, after being 3-0 down at half time.

On 15 October 2013, Suni Olsen retired from International football following a 2014 FIFA World Cup qualification match against Austria.