Terrain traversability analysis is essential for realizing autonomous navigation. This paper proposes a real-time light detection and ranging (LiDAR)-based network for terrain traversability classification in off-road environments. This network incorporates a fast BEV (Bird’s Eye View) feature map generation module, which performs dynamic voxelization, pillar feature encoding and scatter on point cloud, and a traversability completion module that generates accurate and dense BEV traversability maps. The network is trained with dense ground truth labels generated through offline data processing, enabling accurate and dense traversability classification of the surrounding terrain centered on the ego vehicle, with an inference speed reaching 110 + FPS. Finally, we conduct qualitative and quantitative experiments on the RELLIS-3D off-road dataset and SemanticKITTI on-road dataset, which demonstrate the efficiency and accuracy of the proposed approach.