Recently, many researchers have shown interests in anisotropic diffusion methods in image processing. There are two key problems on image restoration techniques based on anisotropic diffusion: one is to build stable diffusion coefficients; the other is to select the optimal stopping time for iterative diffusion process. In this paper, a time-dependent robust anisotropic diffusion method is proposed. The new method is a robust anisotropic diffusion with incorporated time dependent cooling process, and the gradient threshold is the monotonic decreasing function of the time. Thus, the parameters settings and the estimate of the optimal stopping time can be easily resolved. Meanwhile, the proposed method can lessen the over-smooth in image edge features. In order to extent the applicability of the proposed method, we extent the model to the vector-valued form and present time-dependent multispectral robust anisotropic diffusion. Experimental results, performed on several gray images, color images and multispectral remote sensed images, have shown that the time-dependent robust anisotropic diffusion methods can effectively smooth out noise while preserving edge features.