Generalized predictive control (GPC) can be derived in a state space approach as well as in a polynomial approach, and several researches which give relations between these approaches had been discussed. However, strict equivalence between GPC in a polynomial approach and GPC in a state space approach has not been shown so far. Therefore, in this paper, a direct relation between GPC in a state space approach and GPC in a polynomial approach is discussed. According to the result of the paper, GPC in a state space approach with minimal order observer is shown to be exactly equivalent to GPC in the conventional polynomial approach.