Abstract: To solve the loss of image details when removing the stripe noise of hyperspectral images (HSI), a destriping method for hyperspectral images was proposed, which was based on the weighted block sparsity (WBS) regularization and the minimax concave penalty (MCP) constraint (WBS-MCP). WBS-MCP was constructed by employing weighted ℓ_2,1 norm and MCP norm for the sparse features and low-rank constraints, and applying ℓ₁ norm to the edge smoothing constraint of clean image. The alternating direction method of multipliers (ADMM) algorithm was used to iteratively solve the corresponding constraint model, and the clean HSI image was obtained by reconstruction. The experimental results show that the mean equivalent number of look of real HSI improves from 28.45 to 83.47, and the edge retention index increased by 0.056 at least, especially for the aperiodic stripe noise. The adaptive weight was used to update the sparse level, which could enhance the group sparsity and has better performance in maintaining the image edge and enhancing the area smoothness, so that the noise removal has better effect on aperiodic stripe noise.