For the optimization problem of MIMO(multiple input multiple output) radar transmit beampattern under jamming, a new MIMO radar waveform design method based on quadratically spatial and spectral optimization was proposed. Firstly, the proposed method converted the problem of MIMO radar transmit beampattern design into the optimization problem about the covariance matrix of MIMO radar’s transmit spacetime sequences. Based on the fact that MIMO radar transmit beampattern was only decided by the correlation of each element’s transmit waveforms, the computational burden of the spatial optimization of waveforms could be reduced. Furthermore, the nulling towards the jamming direction of the transmit beampattern was broadened by the porder derivative constraint. With the optimized covariance matrix, the randomization method was used to synthesize the actual constant modular waveforms under the criteria of least square to gain on the optimal beampattern. Finally, with the optimized waveforms through spatial optimizing process, a phase flexible diagonal matrix was optimized with the likepower method to achieve the spectral optimization of MIMO radar waveforms based on the fact that MIMO radar transmit beampattern would not be influenced by the change of the initial phase of transmit sequence at a certain moment. And the spectral jamming could be avoided by the spectral optimization of waveforms. Simulation results prove the effectiveness of the proposed method in matching desired beampattern and antijamming.