Landmark localization plays a significant role in craniofacial registration, reconstruction, and authentication. The key challenges for localizing landmarks on point cloud craniofacial models include irregular structures, non-uniform densities, and uncertain local regions. In this paper, we propose an end-to-end regression network that can directly estimate craniofacial landmarks on point cloud models. The proposed network utilizes edge convolution to extract local features and pooling layers to aggregate global features. It realizes the end-to-end regression for landmark localization. Experimental results demonstrate that our method is robust on point clouds with sparse and unevenly distributed sampling. It can produce accurate, controllable, and efficient 3D landmarks.