Since multiple-input multiple-output (MIMO) radar uses multiple antennas to simultaneously transmit diverse waveforms and utilizes multiple antennas to receive the reflected signals, it has many potential advantages over conventional phased-array radar. In this paper, we consider propagator method (PM) for 2-dimensional direction of arrival (DOA) estimation with a low computational load based on cross array in monostatic multiple-input multiple-output (MIMO) radar. The proposed algorithm does not require construction of the cross correlation matrix and its eigen-value decomposition, and also avoids peak searching which requires much computation,so we can greatly reduce the computational complexity; and meanwhile our algorithm can obtain automatically paired the azimuth and elevation angle estimation. Our algorithm has very close estimation performance to estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm in the high signal to noise ratio (SNR) situation, which has much higher complexity than our algorithm. And we also derived the mean square error of the azimuth and elevation angle estimation. The simulation results demonstrate its effectiveness and robustness．