Automatic building facade point cloud semantic segmentation is an important step in 3-D urban building reconstruction. How to correctly segment the components (e.g., windows, walls, and columns) from the building facade is still a challenging task. According to the characteristics of building facade point clouds, we introduce local fusion attention network (LFA-Net), an efficient neural network that learns LFA features from building facade point clouds, for better capturing the local neighborhood structure information of each point. The core of LFA-Net is the LFA module, which consists of three neural units: local graph attention (LGA), local aggregation attention (LAA), and fusion attention (FA). The LFA-Net is the standard encoder-decoder architecture. Experiments demonstrate that our LFA-Net outperforms the state-of-the-art methods on the large-scale building facade point cloud dataset.