Point clouds data, as one kind of representation of 3D objects, are the most primitive output obtained by 3D sensors. Unlike 2D images, point clouds are disordered and unstructured. Hence it is not straightforward to apply classification techniques such as the convolution neural network to point clouds analysis directly. To solve this problem, we propose a novel network structure, named Attention-based Graph Convolution Networks (AGCN), to extract point clouds features. Taking the learning process as a message propagation between adjacent points, we introduce an attention mechanism to AGCN for analyzing the relationships between local features of the points. In addition, we introduce an additional global graph structure network to compensate for the relative information of the individual points in the graph structure network. The proposed network is also extended to an encoder-decoder structure for segmentation tasks. Experimental results show that the proposed network can achieve state-of-the-art performance in both classification and segmentation tasks.