For the 3D face recognition numerous methods have been proposed, but little attention has been given to the local-based representation for the texture map of the 3D models. In this paper, we propose a novel 3D face recognition approach based on locally extracted Geodesic Pseudo Zernike Moment Array (GPZMA) of the texture map when only one exemplar per person is available. In the proposed method, the function of the PZM is controlled by the geodesic deformations to tackle the problem of face recognition under the expression and pose variations. The feasibility and effectiveness investigation for the proposed method is conducted through a wide range of experiments using publicly available BU-3DFE and Bosphorus databases including samples with different expression and pose variations. The performance of the proposed method is compared with the performance of three state-of-the-art benchmark approaches. The encouraging experimental results demonstrate that the proposed method achieves much higher accuracy than the benchmarks in single-model databases.