Naur began his career as an astronomer for which he received his Doctor of Philosophy (Ph.D.) degree in 1957, but his encounter with computers led to a change of profession.

From 1959 to 1969, he was employed at Regnecentralen, the Danish computing company, while at the same time giving lectures at the Niels Bohr Institute and the Technical University of Denmark.

Comprehensive project activity is an integral part of the curriculum, thus presenting theory as an aspect of realistic solutions known primarily through actual experience.

[6] In later years, he was quite outspoken of the pursuit of science as a whole: Naur can possibly be identified with the empiricist school, that tells that one shall not seek deeper connections between things that manifest themselves in the world, but keep to the observable facts.

[7] Naur won the 2005 Association for Computing Machinery (ACM) A.M. Turing Award for his work on defining the programming language ALGOL 60.

[citation needed] Naur published a large number of articles and chapters on astronomy, computer science, issues in society, classical music, psychology, and education.