Compared with the traditional array, the sparse array can offer a larger array aperture with the same number of physical sensors. In this paper, an efficient method to estimate direction of arrivals (DOAs) of two targets based on robust generalized Chinese remainder theorem (RGCRT) for monostatic MIMO radar in sparse array is proposed. Firstly, we employ the all-phase time-shifting phase difference correcting method (AP-TSPDC) to determine the wrapped phases of two targets in the noise environments. And then the improved RGCRT is utilized for the phase unwrapping, enabling accurate DOA estimation for both targets. Besides, the proposed algorithm displays high applicability due to no strict constraint on the array aperture. The future research will extend the proposed algorithm to bistatic radar models. The proposed algorithm is able to achieve high DOA estimation precision with low computational complexity. Computer simulation results confirm the effectiveness and stability of the proposed algorithm.