By taking compressed sensing and sparse representation as theoretical bases, a sparse regularization image inpainting model based on shear wave transform is proposed to reserve the structure characteristics of an image. The model uses shear wave as sparse representation and sparse as a regularization item.Meanwhile, based on variable splitting method, it uses augmented Lagrange method to solve the optimization model. Furthermore, it reduces the complexity of the calculation through alternating direction method of multipliers. The availability of the algorithm is verified by Peak Signal to Noise Radio(PSNR), Structural Similarity Index (SSIM), convergence speed and visual effect. The results indicate that the image inpainting quality by proposed algorithm is better than that by other algorithms, and more optimal PSNR and SSIM can be obtained. The new model has more better performance whether for objective or for visual passitive, moreover, it shows a far quicker convergence rate. It concludes that the algorithm can inpaint images effectively and obtain a better visual effect.