Grabowski, a forward, then he later played as an attacking midfielder or as a winger, started his career with SV Biebrich 1919 and FV Biebrich 1902, both clubs in Wiesbaden. In 1965 he turned over to Eintracht Frankfurt. With this team he won the German Cup in 1974 and 1975 and the UEFA Cup in 1980.
In European Cup competitions he made 40 appearances with nine goals.
He won 44 caps for the German national team and scored five goals. He was member of the German squad in the World Cups of 1966 (in which he did not play), 1970 and 1974. He is known for his versatility, being that he can play on either side of midfield.