We propose a new non-convex first-order variational model for the image super-resolution problem. The model employs a recently developed regularizer that has proven to be effective in image restoration. Due to this regularizer, the salient feature of our model lies in the fact it can construct sharp edges in those generated super-resolution images from lower-resolution ones. Moreover, it also helps suppress the staircase effect. The maximum-minimum principle is proved, which indicates that there is no need to impose hard constraints on the objective function. Alternating direction method of multipliers with spectral penalty selection (spsADMM) is utilized to minimize the associated functional. Cartoon and real gray and color images are tested to demonstrate the features of our model to show the comparison with state-of-the-art image super-resolution techniques.