In this paper, a compressive sensing-based data fitting direction-of-departure/direction-of-arrival (DOD/DOA) estimation algorithm is proposed to apply the superior performance of compressive sensing method to the bistatic MIMO sonar systems. The algorithm proposed in this paper optimizes the output data via convex optimization-based sparse recovery, so that it is possible to estimate the DOD and the DOA for each target accurately. In order to minimize the amount of computation, the cost function with constraint condition is implemented in this paper. Furthermore, the constraint condition parameter of the cost function is analytically derived. Through various simulations, it is shown that the superior DOD and DOA estimation performance of the proposed algorithm and that the analytical derivation of the constraint condition parameter is useful for determination of regularization parameter.