Abstract: 3D face similarity is a critical issue in computer vision, computer graphics and face recognition and so on. Since Fréchet distance is an effective metric for measuring curve similarity, a novel 3D face similarity measure method based on Fréchet distances of geodesics is proposed in this paper. In our method, the surface similarity between two 3D faces is measured by the similarity between two sets of 3D curves on them. Due to the intrinsic property of geodesics, we select geodesics as the comparison curves. Firstly, the geodesics on each 3D facial model emanating from the nose tip point are extracted in the same initial direction with equal angular increment. Secondly, the Fréchet distances between the two sets of geodesics on the two compared facial models are computed. At last, the similarity between the two facial models is computed based on the Fréchet distances of the geodesics obtained in the second step. We verify our method both theoretically and practically. In theory, we prove that the similarity of our method satisfies three properties:reflexivity, symmetry, and triangle inequality. And in practice, experiments are conducted on the open 3D face database GavaDB, Texas 3D Face Recognition database, and our 3D face database. After the comparison with iso-geodesic and Hausdorff distance method, the results illustrate that our method has good discrimination ability and can not only identify the facial models of the same person, but also distinguish the facial models of any two different persons.