How to learn long-range dependencies from 3D point clouds is a challenging problem in 3D point cloud analysis. Addressing this problem, we propose a global attention network for point cloud semantic segmentation, named as GA-Net, consisting of a point-independent global attention module and a point-dependent global attention module for obtaining contextual information of 3D point clouds in this paper. The point-independent global attention module simply shares a global attention map for all 3D points. In the point-dependent global attention module, for each point, a novel random cross attention block using only two randomly sampled subsets is exploited to learn the contextual information of all the points. Additionally, we design a novel point-adaptive aggregation block to replace linear skip connection for aggregating more discriminate features. Extensive experimental results on three 3D public datasets demonstrate that our method outperforms state-of-the-art methods in most cases.