Grosheide worked as a teacher and education administrator for Protestant Reformed special schools from November 1954 until September 1963.

After the election of 1963 Grosheide was appointed State Secretary for Education, Arts and Sciences in the Cabinet Marijnen, taking office on 3 September 1963.

After the election of 1967 Grosheide remained State Secretary for Education and Sciences in the Cabinet De Jong, taking office on 5 April 1967.

Grosheide remained active in national politics, in January 1974 he was nominated as Mayor of Rijswijk, taking office on 1 February 1974.

Grosheide was appointed Special Coordinator for European Immigration an Asylum and Deputy Secretary-General of the Ministry of Justice on 1 January 1991.