In order to further improve the effect of sidelobe suppression, a synthetic aperture radar image sidelobe suppression method based on wavelet transform and spatial variant apodization is proposed in this paper. 2D wavelet decomposition is carried out for the real and imaginary parts of the complex image after imaging respectively, and the sub-channels obtained after the decomposition are then implemented by the spatial variant apodization sidelobe suppression algorithm. The real part data and imaginary part data are reconstructed by using the sub-channel data after the sidelobe suppression. Then, the reconstructed real part data and the imaginary part data are subjected again to spatial variant apodization sidelobe suppression respectively. Finally, the complex image after wavelet transform spatial variant apodization sidelobe suppression is obtained. Experimental results show that the proposed method can effectively suppress the sidelobe of the image without losing the image resolution. Therefore, this proposed method is an effective sidelobe suppression method for synthetic aperture radar images.