Abstract: During image acquisition, hyperspectral data are easily contaminated by noise, which affects image quality and reduces the accuracy of subsequent applications. To solve this problem, a hyperspectral image-denoising model based on nonconvex low-rank tensor approximation and total variation is proposed. The nuclear norm of the frame tensor shrinks each singular value equally, which means that the main information of the image cannot be preserved. Therefore, the frame tensor L_γ is proposed to approximate the global low rank of the hyperspectral image and reduce the shrinkage of large singular values to preserve the main information of the image. It is combined with the spatial spectral total variation to fully explore the low-rank characteristics of hyperspectral images while maintaining the local smoothness of the spatial spectra as well as to remove Gaussian and striping noise. An efficient augmented Lagrange multiplier (ALM) algorithm is developed to solve this model. The simulation and real data experiments show that the proposed model outperforms other algorithms in terms of denoising performance and image visual effect, and the contour curve after denoising is not excessively smooth.