Blind zones and ambiguities in range and velocity measurement are two important issues in the traditional pulse-Doppler radar. By generating random deviations with respect to a mean pulse repetition interval (PRI), which is converted to the restricted isometry property of the observing matrix, the proposed random PRI radar, based on the compressed sensing theory, provides a new way for moving target detection. In order to solve the problems of 'straddling loss' and clutter perturbation, a precise velocity measurement by local dictionary fractionization is proposed according to the iterative idea and the clutter is suppressed by modifying the optimization problem of CS. The simulation results demonstrate that this scheme has high performance of velocity measurement and clutter suppression.