To solve the problem that the accuracy of the acquired SAR image information is reduced due to the interference of external environment, a low-rank approximation method for high-order SAR images based on Tensorial Singular Value Decomposition (TSVD) is proposed.Firstly, on the basis of classical Singular Value Decomposition(SVD), the classical two-dimensional matrix is extended to the tensorial high-order matrix by using the neighborhood selection method.Secondly, the classical matrix algorithm is extended to the algorithm related to the tensorial matrix by using “t-product” model, and the specific implementation process of TSVD is obtained.Finally, the performance of low-rank approximation under the conditions of TSVD is compared with that of the classical SVD by using structural similarity and PSNR.The simulation results show that, compared with the classical SVD, the TSVD fully considers the interaction and spatial structure between image pixels, and with the expansion of the order of the tensorial matrix, the higher the similarity of image structure and the higher the PSNR.The method can be applied to the low-rank approximation and reconstruction of high-order images.