In this paper, we consider a bistatic multiple-input multiple-output (MIMO) radar. We propose a reduced complexity algorithm to estimate the direction-of-arrival (DOA) and direction-of-departure (DOD) for moving target. We show that the calculation of parameter estimation can be expressed in terms of one-dimensional fast-Fourier-transforms which drastically reduces the complexity of the optimization algorithm. The performance of the proposed algorithm is compared with the two-dimension multiple signal classification (2D-MUSIC) and reduced-dimension MUSIC (RD-MUSIC) algorithms. It is shown by simulations, our proposed algorithm has better estimation performance and lower computational complexity compared to the 2D-MUSIC and RD-MUSIC algorithms. Moreover, simulation results also show that the proposed algorithm achieves the Cramer-Rao lower bound.