Abstract: Each pixel of a tensor image is usually characterized by a 3-order positive definite matrix. Currently, existing methods of denoising tensor images usually regard the data as multi-channel images, which is likely to destroy the structure of positive definite matrices of the image and some information will be missed possibly. This paper addresses the problem of denoising complex tensor images. More precisely, we extend the anisotropic diffusion model, also known as P-M model, from scalar or vector images to complex tensor ones. The proposed method can be applied to remove speckle noises in PolSAR images. In contrast with existing denosing algorithms, our method is better at suppressing the effects of speckles while preserving edges.