The weaknesses between L1 norm minimization estimator and L2 norm minimization estimator in the traditional super resolution reconstruction problem are analyzed. In this paper, L1 norm and L2 norm are weighted and combined to measure the data fidelity term, and based on an approximate total variation regularization method [1][2], a robust weighted and combined super resolution reconstruction algorithm is proposed. Simulation experiments show that this method not only enhances the quality of the restoration images and has better edge-preserving capability, but also efficiently removes the visual artifacts and is robust to noise.