An algorithm of fingerprint minutiae extraction using Hessian matrix was proposed in order to overcome the shortcoming of Direct Gray-level Minutiae Detection (DGMD) proposed by Maio,etc.,which had the failure of minutiae extraction as a result of abrupt changes of the fingerprint ridge curvature. Combining the characteristics of Hessian matrix eigenvectors and the geometry direction of fingerprint,the proposed algorithm tracked the ridges of fingerprint and extracted minutiae accurately. The experimental results based on FVC2000 show that the proposed algorithm can track the fingerprint ridge whose curvature changes abruptly. So the algorithm has achieved the total correct minutiae extraction rate of 95.5%. Moreover,the algorithm has better robustness and accuracy than DGMD algorithm and Hessian matrix algorithm.