In this paper, we propose a graph neural network to detect objects from a LiDAR point cloud. Towards this end, we encode the point cloud efficiently in a fixed radius near-neighbors graph. We design a graph neural network, named Point-GNN, to predict the category and shape of the object that each vertex in the graph belongs to. In Point-GNN, we propose an auto-registration mechanism to reduce translation variance, and also design a box merging and scoring operation to combine detections from multiple vertices accurately. Our experiments on the KITTI benchmark show the proposed approach achieves leading accuracy using the point cloud alone and can even surpass fusion-based algorithms. Our results demonstrate the potential of using the graph neural network as a new approach for 3D object detection. The code is available https://github.com/WeijingShi/Point-GNN.