Abstract: This paper proposes a nonlinear diffusion filter to enhance fingerprint image and extract the minutiae according to the characteristic of the fingerprint. The algorithm uses the structure tensor to construct diffusion tensor, and makes the filter diffuse along the ridge direction. In order to improve the computing efficiency, according to the discrete format of the diffusion tensor in a window size of (2n+1)×(2n+1), the diffusion filter is split into 4n directions, after that, in each direction the fingerprint enhancement image is computed with Thomas-Gaussian elimination algorithm. The advantage of this algorithm is to connect the breaking ridges in an effective way, and without changing the continuity and singularity of the ridge. Experiments on NIST27 and FVC2002 databases show that the enhancement algorithm based on nonlinear diffusion filter could improve the performance of extracting minutiae and correct fingerprint matching ratio.