In this paper, we present a novel approach for fusing shape and texture local binary patterns (LBPs) on a mesh for 3D face recognition. Using a recently proposed framework, we compute LBP directly on the face mesh surface, then we construct a grid of the regions on the facial surface that can accommodate global and partial descriptions. Compared with its depth-image counterpart, our approach is distinguished by the following features: 1) inherits the intrinsic advantages of mesh surface (e.g., preservation of the full geometry); 2) does not require normalization; and 3) can accommodate partial matching. In addition, it allows early level fusion of texture and shape modalities. Through experiments conducted on the BU-3DFE and Bosphorus databases, we assess different variants of our approach with regard to facial expressions and missing data, also in comparison to the state-of-the-art solutions.