Aiming at the problems that the detection accuracy of small objects such as cyclists and pedestrians in Three-Dimensional （3D） object detection is low， and it is difficult to adapt to complex urban road conditions， a 3D object detection network based on self-attention mechanism and graph convolution was proposed. Firstly， in order to obtain more discriminative small object features， self-attention mechanism was introduced into the backbone network to make the network more sensitive to small object features and improve the ability to extract network features. Secondly， a feature fusion module was constructed based on the self-attention mechanism to further enrich the information of shallow network and enhance the feature expression ability of deep network. Finally， dynamic graph convolution was used to predict the boundary box of the object， improving the accuracy of object prediction. The proposed network was tested on KITTI dataset， and compared to eight major networks such as TANet （Triple Attention Network） and IA-SSD （Instance-Aware Single-Stage Detector）. The experimental results show that the pedestrian detection accuracy of the proposed network is increased by 12.12， 13.82 and 11.03 percentage points compared with TANet， which has the suboptimal pedestrian detection accuracy， under three difficulty levels of simple， medium，and difficult degrees； the cyclist detection accuracy of the proposed network is 3.06 and 5.34 percentage points higher than that of IA-SSD under medium and difficult degrees. In summary， the network proposed in this paper can be better applied to small object detection tasks.