The issue of direction of departure (DOD) and direction of arrival (DOA) estimation for bistatic coprime multiple-input multiple-output (MIMO) radar is discussed, and an algorithm based on combined estimation of signal parameters via rotational invariance technique (ESPRIT) is proposed. The transmitter and receiver both adopt coprime arrays with large inter-element spacing, which can avoid mutual coupling problem. Based on the uniformity of the subarrays in coprime arrays, ESPRIT is employed to obtain an arbitrary ambiguous estimation, which then is used to recover all the other estimations by realizing the relationships between them. The DOD and DOA estimation can be uniquely determined by finding the coincide estimations from two subarrays. The proposed algorithm has low complexity, and it can achieve better estimation performance than conventional methods. Simulation results verify the effectiveness of the proposed algorithm.