The point cloud learning community is witnesses a modeling shift from CNNs to Transformers, where pure Transformer architectures have achieved top accuracy on the major learning benchmarks. However, existing point Transformers are computationally expensive since they need to generate a large attention map, which has quadratic complexity (both in space and time) with respect to input size. To solve this shortcoming, we introduce Patch ATtention (PAT) to adaptively learn a much smaller set of bases upon which the attention maps are computed. By a weighted summation upon these bases, PAT not only captures the global shape context but also achieves linear complexity to input size. In addition, we propose a lightweight Multi-Scale aTtention (MST) block to build attentions among features of different scales, providing the model with multi-scale features. Equipped with the PAT and MST, we construct our neural architecture called PatchFormer that integrates both modules into a joint framework for point cloud learning. Extensive experiments demonstrate that our network achieves comparable accuracy on general point cloud learning tasks with 9.2× speed-up than previous point Transformers.