Premier of the Soviet Union is the commonly used English term for the offices of Chairman of the Council of People's Commissars (or Sovnarkom)(1923-1946) and Chairman of the Council of Ministers of the USSR (1946-1991) (Председатель Совета Министров СССР) - who was the head of government in the Soviet Union.
However, the real power in the USSR was in the Politburo. After Lenin's death the key position in the Politburo and the country was the General Secretary. Some Soviet leaders held both positions at the same time. See also List of leaders of the Soviet Union
Chairman of the Council of People's Commissars
Chairman of the Council of Ministers of the USSR
Prime Minister of the USSR