This paper proposed an approach to extraction of invariant surface descriptor for multi-view 3D face models. In this approach, 3D facial data were first normalized to the same location, scale and orientation. The normalized faces were then cropped to highlight the most significant region. Within this region, six 3D invariant moments were finally calculated and defined as a descriptor. The proposed invariant descriptor has been compared to the descriptor presented by Xu et al. on the Face Recognition Grand Challenge (FRGC, version 2.0) database. The results demonstrated that our descriptor has higher invariance and better differentiation ability, and therefore can be applied to identification and authentication of multi-view 3D face models.