Abstract: This paper investigates joint optimization of beampattern synthesis and spectral compatibility of multiple-input multiple-output (MIMO) radar transmit waveform under constant modulus constraint. In complex electromagnetic environments, it is necessary to consider the spectrum compatibility and flexibility in the congested frequency band to avoid poor transmission performance of the communication system in the adjacent frequency band. In this paper, the joint optimization problem is modeled as a weighted mean square error cost function constrained by constant modulus, which is non-convex and non-smooth. In each step of the iterative optimization algorithm, firstly update the matching coefficient of the current step and scale the cost function to construct a majorization function. Next, the majorization function is optimized to obtain a waveform correspond to a smaller cost function value. The performance of the proposed algorithm has a good performance on beampattern synthesis and spectrally compatibility, it also has a small amount of calculation. Simulation and numerical results prove the effectiveness of the proposed method.