The recent success of neural networks enables a better interpretation of 3D point clouds, but processing a large-scale 3D scene remains a challenging problem. Most current approaches divide a large-scale scene into small regions and combine the local predictions together. However, this scheme inevitably involves additional stages for pre- and post-processing and may also degrade the final output due to predictions in a local perspective. This paper introduces Fast Point Transformer that consists of a new lightweight self-attention layer. Our approach encodes continuous 3D coordinates, and the voxel hashing-based architecture boosts computational efficiency. The proposed method is demonstrated with 3D semantic segmentation and 3D detection. The accuracy of our approach is competitive to the best voxel-based method, and our network achieves 136 times faster inference time than the state-of-the-art, Point Transformer, with a reasonable accuracy trade-off.