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We present an anisotropic 3D mesh smoothing method which is effective and feature-preserving. The algorithm is originated from bilateral mesh denoising and improved in two aspects. Firstly, the geodesic distance, instead of Euclidean distance, is adopted for the selection of neighboring vertices. Secondly, the way to calculate smoothing offsets is adjusted and a normal weight is introduced. Compared with previous smoothing methods, our method doesn't need to repeat the smoothing operations and could preserve the features of original model with relatively faster speed. Finally, we provide a series of examples to graphically and numerically demonstrate the quality of our results.