Point cloud based retrieval for place recognition is still a challenging problem since the drastic appearance changes of scenes due to seasonal or artificial changes in the environments. Existing deep learning based global descriptors for the retrieval task usually consume a large amount of computational resources ( e.g ., memory), which may not be suitable for the cases of limited hardware resources. In this paper, we develop an efficient point cloud learning network (EPC-Net) to generate global descriptors of point clouds for place recognition. While obtaining good performance, it can greatly reduce computational memory and inference time. First, we propose a lightweight but effective neural network module, called ProxyConv, to aggregate the local geometric features of point clouds. We leverage the adjacency matrix and proxy points to simplify the original edge convolution for lower memory consumption. Then, we design a lightweight grouped VLAD network to form global descriptors for retrieval. Compared with the original VLAD network, we propose a grouped fully connected layer to decompose the high-dimensional vectors into a group of low-dimensional vectors, which can reduce the number of parameters of the network and maintain the discrimination of the feature vector. Finally, we further develop a simple version of EPC-Net, called EPC-Net-L, which consists of two ProxyConv modules and one max pooling layer to aggregate global descriptors. By distilling the knowledge from EPC-Net, EPC-Net-L can obtain discriminative global descriptors for retrieval. Extensive experiments on the Oxford dataset and three in-house datasets demonstrate that our method achieves good results with lower parameters, FLOPs, GPU memory, and shorter inference time. Our code is available at https://github.com/fpthink/EPC-Net.