Wave band selection is an effective means to reduce the dimension and much redundancy of hyperspectral data, and it is an important prerequisite for pixel classification of hyperspectral images. It is a complex combinatorial optimization problem in essence, and it is difficult to get satisfactory solution by traditional search methods. To solve the above problems, a method of hyperspectral band selection based on golden sine and chaotic the spotted hyena optimization algorithm (GSSHO) is proposed. Firstly, chaos strategy is used to initialize the spotted hyena population to improve the randomness and diversity of the population. Secondly, golden sine algorithm is used to improve the original spotted hyena optimization (SHO) algorithm to search individual position update mode to improve the global search ability of the algorithm. Finally, a fitness function combining classification accuracy and band number is designed to evaluate the optimization performance of the algorithm. On hyperspectral remote sensing data sets, this method is compared with other advanced optimization algorithms. The experimental results show that the number of bands selected in this algorithm is close to one tenth of the original band, and the classification accuracy of Pavia Centre data set is up to 99.08%, which is better than those of other comparison methods. It can find the optimal solution with more reasonable convergence direction, and the number of selected bands is less, and the classification accuracy is higher. It is an efficient method for selecting wave band.