The autocorrelation and crosscorrelation sidelobes of multiple input multiple output (MIMO) radar transmit waveforms seriously affect the performance of moving targets detection. To solve this problem, this paper analyzes the influence of waveform autocorrelation and cross correlation on clutter suppression, and proposes a clutter suppression method based on tensor compression sensing. This method can effectively eliminate the impact of nonorthogonal waveforms on the clutter suppression of MIMO radar by reconstructing the clutter spectrum. Furthermore, the radar parameters and environment dynamic database (EDDB) are used to calculate the a priori position of the clutter ridges. A priori clutter position constraint is added to the clutter spectrum reconstruction to effectively reduce the clutter pseudo peaks generated by the compressionaware algorithm. Simulation results show that the method can effectively suppress clutter in the case of small samples, and the computational complexity is low.