Born in Adelaide on 3 January 1932, Peter's father was Colonel JS Grimshaw, MC, and was Commissioner of the Royal Papua and New Guinea Constabulary from 1947 to 1954, with Peter spending part of his early life in Papua New Guinea.

Educated at Unley High School he later studied for an Arts degree from the University of Queensland and obtained a Master’s degree in Education (Administration) from the University of New England. From 1949 to 1957 Peter served in the Department of Civil Aviation in Papua New Guinea and also joined the Papua New Guinea Volunteer Rifles in which he was commissioned.

Peter joined the staff of the Australian National University as Business Manager in 1964 and held
that post in different capacities until his retirement in 1997.While at the ANU he continued his historical studies and just before his death he completed a manuscript on the history of the Papua New Guinea constabulary.