Three-dimensional face recognition is an important part of the field of computer vision. Point clouds are widely used in the field of 3D vision due to the simple mathematical expression. However, the disorder of the points makes it difficult for them to have ordered indexes in convolutional neural networks. In addition, the point clouds lack detailed textures, which makes the facial features easily affected by expression or head pose changes. To solve the above problems, this paper constructs a new face recognition network, which mainly consists of two parts. The first part is a novel operator based on a local feature descriptor to realize the fine-grained features extraction and the permutation invariance of point clouds. The second part is a feature enhancement mechanism to enhance the discrimination of facial features. In order to verify the performance of our method, we conducted experiments on three public datasets: CASIA-3D, Bosphorus, and Lock3Dface. The results show that the accuracy of our method is improved by 0.7%, 0.4%, and 0.8% compared with the latest methods on these three datasets, respectively.