The mission of speckle filtering is more intricate for a polarimetric synthetic aperture radar (SAR) system than for a single polarization SAR system. A new speckle filter that employs nonlinear anisotropic diffusion is proposed. The speckle filtering principles in a polarimetric SAR system are thoroughly investigated. Our study demonstrates that preservation of polarimetric properties and reduction of speckle level are very important clauses among those principles. Anisotropic diffusion outperforms window-based filters because it utilizes a diffusion tensor that can bias the direction of diffusion toward the orientation of interesting features. The procedure of diffusion is iterative, so it can lead to a gradual alleviation of speckle noise. The parameters for diffusion are flexible and adjustable, thus the filtering results are controllable according to the requirements of specific applications. Multidimensional and vector-valued model is combined with local statistics based on polarimetric SAR configuration. The experimental results on electromagnetics institute synthetic aperture radar (EMISAR) datasets show that the proposed filter has good performance in speckle reduction and preservation of polarimetric properties.