Suurbier was born in Eindhoven. He made his debut for Ajax Amsterdam when he was 19 and played with them for 13 years, all throughout the most successful era until 1977 when he was 32 years old. Usually a right back, Suurbier was renowned for his pace and stamina. Suurbier was a big part of the 70’s “total football” team the “Twelve Apostles” of Ajax Amsterdam led by Johan Cruijff, which lifted the UEFA European Cup three times in a row. In 1977, he moved to FC Schalke 04 with the collaboration of the football manager Békeffy Jenő for one season.
In 1979, Suurbier transferred to the Los Angeles Aztecs of the North American Soccer League. He played three seasons in Los Angeles before moving to the San Jose Earthquakes for the 1982 season. In the fall of 1982, the team was renamed the Golden Bay Earthquakes and entered the Major Indoor Soccer League. He retired at the end of the season to become an assistant coach with the Earthquakes.
Suurbier played 60 matches and scored three goals for the Netherlands national team from 1966 to 1978. He played in both the 1974 and 1978 World Cups[3] where the Dutch finished second, and also the 1976 UEFA European Football Championship.