Hyperspectral images (HSIs) are polluted by a large amount of mixed noise during the acquisition process, which affects the performance of subsequent applications of remote sensing images. Therefore, restoring clean HSI from the mixed noise is an important preprocessing step. In this study, a hyperspectral mixed noise image restoration model based on nonconvex low-rank tensor decomposition and group-sparse total variational regularization is proposed. On the one hand, by using logarithmic tensor nuclear norm to approximate the low-rank characteristics of the HSI, the inherent tensor structure of hyperspectral data can be utilized, and the shrinkage of larger singular values can be reduced to preserve more detailed features of the image. On the other hand, the group sparse total variational regularization can be used to enhance the spatial sparsity of the HSI and correlation between adjacent spectra. ADMM algorithm is used to solve the problem, and an experiment shows that the algorithm converges easily. In simulated and real hyperspectral image experiments, this method performs better in removing HSI mixed noise when compared to other methods.