Summary: We introduce and investigate the modified total variation (TV)-Stokes model for two classical image processing tasks, i.e., image restoration and image inpainting. The modified TV-Stokes model is a two-step model based on a TV minimization in each step and the use of geometric information of the image. In the first step, a smoothed and divergence-free tangential field of the given image is recovered, and in the second step, the image is reconstructed from the corresponding normals. The existence and the uniqueness of the solution to the minimization problems are established for both steps of the model. Numerical examples and comparisons are presented to illustrate the effectiveness of the model.