A novel fingerprint encryption algorithm based on topological structure of fingerprint minutiae is presented in this paper. The encryption algorithm randomly selects three different points on the infinite plan, which form a triangle and do not belong to any fingerprint feature points, as the fingerprint encryption keys. The distance between the fingerprint feature points and the three selected points is taken as encrypted value, which is calculated for every fingerprint feature point until all the feature points are encrypted, and finally the fingerprint encryption value is obtained. Compared with the previous fingerprint encryption algorithms, the advantage of the proposed algorithm is to expand the selection range of the initial value of the key and the key space, which makes the brute force more difficult. The encryption calculation method is simple and its complexity is low, the encryption efficiency for a large amount of fingerprint data is improved.