In recent years, with the rapid development of remote sensing technology, Hyperspectral Images (HSI) have attracted more and more attention. Compared with full color and multi-spectrum remote sensing, hyperspectral remote sensing has higher spectral resolution, which greatly improves the recognition ability of surface coverage and the accuracy and reliability of ground object analysis. With the continuous updating of sensors, people can obtain remote sensing images of different space resolution and spectral resolution on different aviation and aerospace remote sensing platforms. Compared with previous remote sensing technology, hyperspectral remote sensing has the characteristics of combining maps and a series of bands from visible light to infrared and even thermal infrared. Especially in the case of weak information on the ground, hyperspectralremote sensing has the advantages of identifying weak information and quantitative detection. The development of hyperspectral remote sensing technology to meet the needs of military and civilian technology is very necessary and practical to carry out research in this field. HSI consists of different intensities, which represents the radiation points of hundreds of discrete wave bands captured by the sensor. Compared with traditional images, HSI helps to provide more reliable expressions for real scenes, so it is often better in various computer visual tasks, such as classification, super resolution, compression perception, mineral exploration, etc. However, under actual situation, HSI is always seriously affected by noise. These noises are usually caused by sensor sensitivity, photon effects, light conditions, and calibration errors. Therefore, HSI denoising is a key problem, and solving this problem can greatly improve the performance of subsequent HSI processing tasks, which is an important and challenging research topic. Around this topic, many experts have proposed various noise models and achieved good results. By studying the existing noise models and analysis of the characteristics of HSI, a new HSI denoising model is established in this paper. Compared with the previous models, the ability to remove mixed noise and retain image details has been strengthened. By analyzing the structural characteristics of HSI, a HSI denoising model based on tensor low-rank decomposition, mixed space-spectral gradient domain low-rank decomposition and group sparse prior is proposed in this study. Firstly, the high-order gradient is introduced to fully explore the intrinsic contact between the high-order differential direction. The HSI is converted from the original domain to the gradient domain by using 1st and 2nd gradient operators, and the weighted norm is established on the mixed gradient tension to explore the gradient group sparse prior of the HSI. Secondly, the low-rank priori of HSI is explored in both gradient domain and the original domain. The low-rank property of the gradient domain is proved by the low-rank theory of transform domain, and it is constrained by the minimization of nuclear norm. The classical tensor Tucker decomposition method is then used to ensure the low-rank prior to the original domain of HSI. The new model makes full use of the prior information of HSI, effectively removes the mixed noise, and greatly improves the performance of subsequent HSI processing tasks. This technique is of great practical significance to meet military and civilian needs. Finally, through a lot of experiments on simulated datasets and real datasets, the superiority of the new model in the field of hyperspectral image denoising is proved. Compared with the suboptimal model, the average peak signal to noise ratio and the average structural similarity index of the proposed model are improved by 5.35 dB and 0.009 respectively.