Abstract: A convex variational model is proposed for multi-frame image super-resolution with sparse representation regularization. The regularization term constrains the underlying image to have a sparse representation in a proper frame. The fidelity term restricts the consistency with the measured image in terms of the data degradation model. The characters of the optimal solution to the model are analyzed. Furthermore, a fixed-point numerical iteration algorithm is proposed to solve this convex variational problem based on the proximal forward-backward splitting method for monotone operator. At every iteration, the forward (explicit) gradient step for the fidelity term and the backward (implicit) step for regularization term are activated separately, thus complexity is decreased rapidly. The convergence of the numerical algorithm is studied and a continuation strategy is exploited to accelerate the convergence speed. Numerical results for optics and infrared images are presented to demonstrate that our super-resolution model and numerical algorithm are both effective.