Curb detection provides road boundary information and is important to road detection. Howev-er, curb detection is challenging due to the problems such as various curb shapes, colour, disconti-nuity. In this work, a novel learning-based method for curb detection is proposed using Lidar point clouds, considering that Lidars are not sensitive to illumination and are relatively stable to weather conditions. A deep neural network, named EdgeNet, is constructed and trained, which handles point clouds in an end-to-end way. After EdgeNet is properly trained, curb points are then segmen-ted in the neural network output. In order to train, a curb point annotation algorithm is also designed to generate training dataset. The curb detection method works well with different road scenarios in-cluding intersections. The experimental results validate the effectiveness and robustness of this curb detection method.