Accurate registration is an essential prerequisite for analysis and applications involving remote sensing imagery. It is usually difficult to extract enough matching points for inter-band registration in hyperspectral imagery due to the different spectral responses for land features in different image bands. This is especially true for non-adjacent bands. The inconsistency in geometric distortion caused by topographic relief also makes it inappropriate to use a single affine transformation relationship for the geometric transformation of the entire image. Currently, accurate registration between spectral bands of Zhuhai-1 satellite hyperspectral imagery remains challenging. In this paper, a full-spectrum registration method was proposed to address this problem. The method combines the transfer strategy based on the affine transformation relationship between adjacent spectrums with the differential correction from dense Delaunay triangulation. Firstly, the scale-invariant feature transform (SIFT) extraction method was used to extract and match feature points of adjacent bands. The RANdom SAmple Consensus (RANSAC) algorithm and the least square method is then used to eliminate mismatching point pairs to obtain fine matching point pairs. Secondly, a dense Delaunay triangulation was constructed based on fine matching point pairs. The affine transformation relation for non-adjacent bands was established for each triangle using the affine transformation relation transfer strategy. Finally, the affine transformation relation was used to perform differential correction for each triangle. Three Zhuhai-1 satellite hyperspectral images covering different terrains were used as experiment data. The evaluation results showed that the adjacent band registration accuracy ranged from 0.2 to 0.6 pixels. The structural similarity measure and cosine similarity measure between non-adjacent bands were both greater than 0.80. Moreover, the full-spectrum registration accuracy was less than 1 pixel. These registration results can meet the needs of Zhuhai-1 hyperspectral imagery applications in various fields.