Hyperspectral images have a higher spectral and spatial resolution and thus can differentially diagnose the spectral characteristics of ground objects. However, when acquiring hyperspectral images, the vibration of the platform often distorts the spectral image, which seriously affects the accuracy and reliability of spectral images in applications. This paper proposes a dynamic chaos disturbance genetic algorithm capable of restoring vibration-blurred hyperspectral images. Compared with ordinary genetic algorithms, this algorithm does not converge prematurely and can recover images more accurately with improved spectral quality. Based on the degradation principle of vibration-blurred images, we start by generating the mapping relationship between the vibration blurred image and the clear image and the point spread function of the vibration blurred image. Based on the nonlinear and chaotic characteristics of the degradation of the vibration blurred image, tent mapping is used to generate the initial chaotic population, which enhances the global search ability of the genetic algorithm. Specifically, we use Chebyshev mapping to chaotically perturb the outstanding individuals, thus enhancing the genetic algorithm's local search ability. The three-dimensional hyperspectral image is tiled into a two-dimensional image, and the image correlation of adjacent spectral channels is used to restore the three-dimensional hyperspectral data. To verify the performance of our method, we run two sets of image restoration simulations using data cubes provided by the Australian airborne Hymap imaging spectrometer. The method in this paper is compared with the data-of-art spectral image restoration algorithm, and genetic rehabilitation algorithm under multiple criteria, such as non-parametric evaluation method average gray gradient GMG and Laplace operator LS, parametric evaluation method signal-to-noise ratio SNR and incident signal-to-noise ratio PSNR, spectrum uses the spectral information divergence SID and the spectral gradient angle SGA evaluation methods, and it is found that all evaluation indicators can be improved. Compared with the latest spectral restoration algorithm, our method improved the SNR of the image by 60%, PSNR by 10%, GMG by 11%, LS by 11% and reduced the SID by 39%, SGA by 5%. Compared with the original genetic restoration algorithm, our method improved the SNR of the image by 51%, PSNR by 12%, GMG by 33%, LS by 43% and reduced the SID by 39%, SGA by 16%. These results show that our method is highly effective in restoring vibration and blur of spectral image data by significantly improving the clarity of a single band image, and the spectral quality of the spectral data cube.