In view of the sparsity and spatial discrete distribution of lidar point cloud, a graph convolution feature extraction module was designed by combining voxel partition and graph representation, and a 3D lidar point cloud object detection algorithm in view of voxel based graph convolution neural network was proposed. By eliminating the computational redundancy of the traditional 3D convolution neural network, this method not only improved the object detection ability of the network, but also improved the analysis ability of the point cloud topology information. Compared with the baseline network, the detection performance of vehicle, pedestrian and cyclist 3D object detection and bird’s eye view object detection tasks in KITTI public dataset were improved greatly, especially improved with 13.75% precision in 3D object detection task of vehicle at maximal. Experimental results show that the proposed method improves the detection performance of the network and the learning ability of data topological relationship via graph convolution feature extraction module, which provides a new method for 3D point cloud object detection task.