A hybrid error model with L₁ and L₂ norm minimization criteria is proposed in this paper for image/video super-resolution. A membership function is defined to adaptively control the tradeoff between the L₁ and L₂ norm terms. Therefore, the proposed hybrid model can have the advantages of both L₁ norm minimization (i.e. edge preservation) and L₂ norm minimization (i.e. smoothing noise). In addition, an effective convergence criterion is proposed, which is able to terminate the iterative L₁ and L₂ norm minimization process efficiently. Experimental results on images corrupted with various types of noises demonstrate the robustness of the proposed algorithm and its superiority to representative algorithms.