	Luxdorph was born in Copenhagen, the son of Christen Bollesen Luxdorph (died 1669) and Maren Olufsdatter Stafrofski (died1689). He was the elder brother of Peder Luxdorph. His father was employed as economist at Herlufsholm from 1651 and he graduated from the school in 1660. He worked then for a while in the household of professor Peder Resen and from 1662 to 1664 served as a tutor at his old school. In 1775, he accompanied the Danish minister in London Simon de Petkum to England by way of Germany and Belgium. He then spent four years in France.