This project propose, a hyperspectral image (HSI) mixed-noise removal method named Moreau-enhanced total variation (TV) regularized local low-rank matrix recovery (LLRMTV). The rank-fixed matrix recovery is first adopted to separate the low-rank clean HSI patches from the sparse noise. Then, a Moreau-enhanced TV regularized image reconstruction strategy is utilized to ensure the piecewise smoothness of the reconstructed image from the low-rank patches. The proposed Moreau-enhanced TV restoration method involves a nonconvex penalty designed to maintain the convexity of the objective function. Moreover, the proposed model is integrated into an augmented Lagrange multiplier (ALM) algorithm to produce final results, leading to a complete HSI restoration framework. Examples of restoration illustrate the improvement over the typical TV regularization. This project is implemented with MATLAB software.