3D face recognition has shown its potential in many application scenarios. Among numerous 3D face recognition methods, deep-learning-based methods have developed vigorously in recent years. In this paper, an end-to-end deep learning network entitled Sur3dNet-Face for point-cloud-based 3D face recognition is proposed. The network uses PointNet as the backbone, which is a successful point cloud classification solution but does not work properly in face recognition. Supplemented with modifications in network architecture and a few-data guided learning framework based on Gaussian process morphable model, the backbone is successfully modified for 3D face recognition. Different from existing methods training with a large amount of data in multiple datasets, our method uses Spring2003 subset of FRGC v2.0 for training which contains only 943 facial scans, and the network is well trained with the guidance of such a small amount of real data. Without fine-tuning on the test set, the Rank-1 Recognition Rate (RR1) is achieved as follows: 98.85% on FRGC v2.0 dataset and 99.33% on Bosphorus dataset, which proves the effectiveness and the potentiality of our method.