Obstacle detection is one of the essential capabilities for autonomous robots operated on unstructured terrain. In this paper, a novel laser-based approach is proposed for obstacle detection by autonomous robots, in which the Sobel operator is deployed in the edge-detection process of 3D laser point clouds. The point clouds of unstructured terrain are filtered by VoxelGrid, and then processed by the Gaussian kernel function to obtain the edge features of obstacles. The Euclidean clustering algorithm is optimized by super-voxel in order to cluster the point clouds of each obstacle. The characteristics of the obstacles are recognized by the Levenberg–Marquardt back-propagation (LM-BP) neural network. The algorithm proposed in this paper is a post-processing algorithm based on the reconstructed point cloud. Experiments are conducted by using both the existing datasets and real unstructured terrain point cloud reconstructed by an all-terrain robot to demonstrate the feasibility and performance of the proposed approach.