Point sets correspondence concerns with the establishment of point-wise correspondence for a group of 2D or 3D point sets with similar shape description. Existing methods often iteratively search for the optimal point-wise correspondence assignment for two sets of points, driven by maximizing the similarity between two sets of explicitly designed point features or by determining the parametric transformation for the best alignment between two point sets. In contrast, without depending on the explicit definitions of point features or transformation, our paper introduces a novel point correspondence neural networks (PC-Net) that is able to learn and predict the point correspondence among the populations of a specific object (e.g. fish, human, chair, etc) in an unsupervised manner. Specifically, in this paper, we first develop an encoder to learn the shape descriptor from a point set that captures essential global and deformation-insensitive geometric properties. Then followed with a novel motion-driven process, our PC-Net drives a template shape, that consists of a set of landmark points, morph and conform around a target shape object which is reconstructed through decoding the previously characterized shape descriptor. As a result, the motion-driven process progressively and coherently drifts all landmark points from the template shape to corresponding positions on the target object shape. The experimental results demonstrate that PC-Net can establish robust unsupervised point correspondence over a group of deformable object shapes in the presence of geometric noise and missing points. More importantly, with great generalization capability, PC-Net is capable of instantly predicting group point corresponding for unseen point sets.