Blind zones and ambiguities in range and velocity measurement are two important issues in traditional pulse-Doppler radar. By generating random deviations with respect to a mean Pulse Repetition Interval (PRI), this paper proposes a novel algorithm of Moving Target Detection (MTD) based on the Compressed Sensing (CS) theory, in which the random deviations of the PRIare converted to the Restricted Isometry Property (RIP) of the observing matrix. The ambiguities of range and velocity are eliminated by designing the signal parameters. The simulation results demonstrate that this scheme has high performance of detection, and there is no ambiguity and blind zones as well. It can also shorten the coherent processing interval compared to traditional staggered PRI mode because only one pulse train is needed instead of several trains.