To suppress noise of image more efficiently and further improve image visual effects, a noise suppression method of image based on shearlet transform and kernel anisotropic diffusion is proposed. Firstly, a noisy image is decomposed by nonsubsampled shearlet transform(NSST). Then the obtained low-frequency component and high-frequency components are processed by improved total variation (ITV) diffusion and kernel anisotropic diffusion (KAD), respectively. Finally, the noise suppressed image is obtained by synthesizing diffused low-frequency component and high-frequency components through inverse nonsubsampled shearlet transform(INSST). Experimental results are given, in terms of subjective visual effect and two quantitative evaluation indicators such as peak signal to noise ratio (PSNR), structural similarity (SSIM), a comparison is made with three recent proposed noise suppression methods based on wavelet threshold shrinkage and TV, based on nonlinear diffusion in complex contourlet domain, and using TV with adaptive shearlet domain restraint. A large number of experimental results show that the proposed method has stronger noise suppression ability and preserves edge and detail information more completely.