Recently, self-attention networks achieve impressive performance in point cloud segmentation due to their superiority in modeling long-range dependencies. However, compared to self-attention mechanism, we find graph convolutions show a stronger ability in capturing local geometry information with less computational cost. In this paper, we employ a hybrid architecture design to construct our Graph Convolution Network with Attentive Filtering (AF-GCN), which takes advantage of both graph convolution and self-attention mechanism. We adopt graph convolutions to aggregate local features in the shallow encoder stages, while in the deeper stages, we propose a self-attention-like module named Graph Attentive Filter (GAF) to better model long-range contexts from distant neighbors. Besides, to further improve graph representation for point cloud segmentation, we employ a Spatial Feature Projection (SFP) module for graph convolutions which helps to handle spatial variations of unstructured point clouds. Finally, a graph-shared down-sampling and up-sampling strategy is introduced to make full use of the graph structures in point cloud processing. We conduct extensive experiments on multiple datasets including S3DIS, ScanNetV2, Toronto-3D, and ShapeNetPart. Experimental results show our AF-GCN obtains competitive performance.