Point cloud sampling is a less explored research topic for this data representation. The most common sampling methods nowadays are still classical random sampling and farthest point sampling. With the development of neural networks, various methods have been proposed to sample point clouds in a task-based learning manner. However, these methods are mostly generative-based, other than selecting points directly with mathematical statistics. Inspired by the Canny edge detection algorithm for images and with the help of the attention mechanism, this paper proposes a non-generative Attention-based Point cloud Edge Sampling method (APES), which can capture the outline of input point clouds. Experimental results show that better performances are achieved with our sampling method due to the important outline information it learned.