Pevtsov was born in Ustiuzhinskii district, Novgorod province in the estate of a noble family.

He joined the 29th Infantry Tomsk Regiment stationed in Tula in 1862 and was transferred to Poland to suppress the uprising there.

While in St Petersburg he attended meetings of the Imperial Russian Geographical Society, becoming a member of it in 1867.

Pevtsov made astronomical and meteorological observations in his travels and helped produce maps.

In 1878 he led expeditions into western Mongolia and the northern regions of China.