Rock cores are important physical geological material generated during mineral exploration and geological research, which have characterizations of primitiveness, objectivity, and non-renewability. However, rock cores may undergo weathering, fracturing, or even loss in storage and use. Hyperspectral 3D scanning provides an efficient way to manage and store rock cores, which not only reproduces complete appearance features, enables long-term preservation, but also presents rich spectral information of rocks and minerals. In order to obtain high-quality core panorama, a core hyperspectral image distortion correction and stitching method was proposed. Firstly, the main components and its operating procedures of a hyperspectral 3D scanning apparatus for rock cores were introduced. Then, according to the geometric relationship of the scanning apparatus and the Lambert’s cosine law, correction formulas for correcting the radiometric and geometric distortions were derivated in detail. Finally, a weighted average algorithm was used to stitch and fuse core images. The results show that the proposed method can effectively correct both the radiometric and geometric distortions of the rock core images, and yields high-quality core panorama, which has high practical values in engineering projects.