The traditional Convolutional Neural Network (CNN) cannot directly process point cloud data, and the point cloud data must be converted into a multi-view or voxelized grid, which leads to a complicated process and low point cloud recognition accuracy. Aiming at the problem, a new point cloud classification and segmentation network called Linked-Spider CNN was proposed. Firstly, the deep features of point cloud were extracted by adding more Spider convolution layers based on Spider CNN. Secondly, by introducing the idea of residual network, short links were added to every Spider convolution layer to form residual blocks. Thirdly, the output features of each layer of residual blocks were spliced and fused to form the point cloud features. Finally, the point cloud features were classified by three-layer fully connected layers or segmented by multiple convolution layers. The proposed network was compared with other networks such as PointNet, PointNet++ and Spider CNN on ModelNet40 and ShapeNet Parts datasets. The experimental results show that the proposed network can improve the classification accuracy and segmentation effect of point clouds, and it has faster convergence speed and stronger robustness.