Grosser started his career with FC Neuhofen then he went on to MTV München. In 1956 he went to the youth of FC Bayern München. 1958 he played for the first team. 1963 he went to TSV 1860 Munich. With this team he played in the 1965 in the UEFA Cup Winners' Cup versus West Ham United. 1969 he went to Austria and played 164 matches for SV Austria Salzburg. 1975 his career ended.