Abstract: When radar operates on pulse state, it will inevitably encounter the phenomenon of blind speed. The staggered pulse repetition frequency(PRF) is one of the most important methods to suppressing the blind speed. Based on the derivation of frequency response, this paper proposes a method of optimum design for staggered periods, among which the considerations, derivation for several essential parameters of optimal search are also given out in detail. The simulation results, the frequency response figures show that the proposed method can achieve satisfactory suppression performance of blind speed.