Abstract: Transmit beampattern design for Multiple Input Multiple Output (MIMO) radar is obtained by synthesizing the signal covariance matrix, which can be achieved by convex optimization approaches. Due to the high computational complexity, these approaches are not easy for practical implementation. In this paper, a cyclic iterative method for MIMO radar transmit beampattern design is proposed. Based on the weighted least square criterion, signal covariance matrix can be obtained by optimizing the quadratic cost function with respect to its Hermite square root. For the uniform linear array, especially when the sampling grid in normalized spatial frequency is uniform and the weights for grid points are the same, FFT can be used to further reduce the computational complexity of the proposed algorithm. Simulation results show that the resulting beampattern matches the desired pattern closely and the proposed algorithm is efficient for the real time application.