In this note, the problem on approximating a linear periodic system with period N by a periodic model with period M(0 < M < N) is revisited. Different from the existing results, the proposed method is based on state-space representations and the approximation performance is evaluated using H-infinity norms. Under this framework, both finite impulse response (FIR) and infinite impulse response (IIR) periodic systems can be efficiently approximated by using a constructive linear matrix inequality approach. Finally, some numerical examples are given to illustrate the effectiveness of the proposed approach.