Niels Glostrup was born in a small town named Glostrup near Copenhagen, where his father, Simon Jensen, was a priest.
Glostrup was designated as a new suburb along the western Tåstrup-finger of the Copenhagen Finger Plan of 1947.
He grew up with his two brothers, Axel Nielsen (1902–1970) and Povl Erik Nielsen (1909–1995) in Glostrup, 10 kilometres west of Copenhagen.