To address the deficiencies of existing point cloud classification and segmentation methods in processing local features and contextual information, this research proposes a novel network architecture—the COGCN model, which integrating the advantages of convolutional neural network and graph convolutional network, and incorporating the channel and spatial enhanced edge convolution (CSEConv) module and offset attention mechanism. The CSEConv module enhances the extraction of local features from point clouds, while the offset attention module captures contextual features and inter-neighborhood relationships, facilitating more effective information fusion among features. Experimental results on ModelNet40, ShapeNet, and S3DIS datasets show that, the COGCN model has achieved a high accuracy of 93.2% in point cloud classification task, a segmentation mean intersection over union (mIoU) of 86.1% in point cloud segmentation task, and a mIoU of 60.3% in semantic segmentation task, the results are better than the existing algorithms.