Pospelov was born at Konakovo in 1898. He graduated from the Economics Department of the Institute of Red Professors in 1930. He was one of the principal authors of The History of the Communist Party of the Soviet Union (Bolsheviks): Short Course, which served as a basic text on party history in the Stalinist period.
He is also known as the head of the "Pospelov commission" on the investigation of the mass repressions in the Soviet Union, whose findings had laid the basis and the contents of Nikita Khrushchev's "secret speech" On the Personality Cult and its Consequences 
It was only because the Leninist party and its Central Committee, headed by J. V. Stalin, were able ideologically and politically to defeat Trotskyism as an anti-Leninist current, it was only because the entire party rose to the defense of the Leninist doctrine, that the party unity was preserved, and that the split desired by the Trotskyites was prevented and the Communist Party led the Soviet people to the victory of socialism in our country.
Pospelov died in Moscow in 1979 and was buried at the Novodevichy Cemetery.