Point cloud deep learning networks have been widely applied in point cloud classification, part segmentation and semantic segmentation. However, current point cloud deep learning networks are insufficient in the local feature extraction of the point cloud, which affects the accuracy of point cloud classification and segmentation. To address this issue, this paper proposes a local domain multi-level feature fusion point cloud deep learning network. First, dynamic graph convolutional operation is utilized to obtain the local neighborhood feature of the point cloud. Then, relation-shape convolution is used to extract a deeper-level edge feature of the point cloud, and max pooling is adopted to aggregate the edge features. Finally, point cloud classification and segmentation are realized based on global features and local features. We use the ModelNet40 and ShapeNet datasets to conduct the comparison experiment, which is a large-scale 3D CAD model dataset and a richly annotated, large-scale dataset of 3D shapes. For ModelNet40, the overall accuracy (OA) of the proposed method is similar to DGCNN, RS-CNN, PointConv and GAPNet, all exceeding 92%. Compared to PointNet, PointNet++, SO-Net and MSHANet, the OA of the proposed method is improved by 5%, 2%, 3% and 2.6%, respectively. For the ShapeNet dataset, the mean Intersection over Union (mIoU) of the part segmentation achieved by the proposed method is 86.3%, which is 2.9%, 1.4%, 1.7%, 1.7%, 1.2%, 0.1% and 1.0% higher than PointNet, RS-Net, SCN, SPLATNet, DGCNN, RS-CNN and LRC-NET, respectively.