Filtering image by eliminating irrelevant details as could as possible while preserving structure edge and corner becomes very important in the fields such as image processing and computer vision etc. In this paper, we present an Anisotropic Rolling Filter (ARF) for smoothing image while preserving important structure edge and corner. The proposed filter implements an extended cross bilateral filter, in which the range weights are updated in an iterative manner, while the spatial Gaussian weights are computed in anisotropic directions instead of isotropic directions. The anisotropic directions are computed based on structure tensors which are calculated at each pixel to determine structure orientations. Compared with the original rolling guidance filter, it is found that the proposed anisotropic rolling filter has stronger smoothing and structure preserving ability.