The combination of spectral and 3-D elevation information provided by hyperspectral images (HSIs) and Light Detection and Ranging (LiDAR) has gained increased attention in the remote sensing field and enabled numerous applications. While various methods have been proposed to fuse these two data streams in pixel, feature, or decision level, a deeper view into the intrinsic relation of surface geometry, material reflectance, and environment illumination is still lacking. In this article, we present a novel supervoxel-based joint intrinsic decomposition framework for HSIs and LiDAR. First, we proposed a novel intrinsic scene model for HSIs and LiDAR point cloud, which tells how we can map LiDAR point cloud into HSI pixels with point-cloud-level normals, reflectance, and incident light direction. Then, we extract supervoxels from the LiDAR point cloud using a graph-based supervoxel method. Finally, we formulate the intrinsic decomposition problem within a supervoxel-based framework which can be optimized effectively and efficiently. The outputs of the proposed model are intrinsic scene properties like incident light direction and point-cloud-level hyperspectral reflectance, with which we can then generate intrinsic hyperspectral point cloud (IHSPC) where each point possesses not only 3-D coordinates and normals but also the reflectance over each wavelength. The performance of our approach is demonstrated with both synthetic and real data.