Based on image sparse representation in the shearlet domain, we proposed a L1/2 sparsity regularized unconvex variation model for image super-resolution. The L1/2 regularizer term constrains the underlying image to have a sparse representation in shearlet domain. The fidelity term restricts the consistency with the measured imaged in terms of the data degradation model. Then, the variable splitting algorithm is used to break down the model into a series of constrained optimization problems which can be solved by alternating direction method of multipliers. Experimental results demonstrate the effectiveness of the proposed method, both in its visual effects and in quantitative terms.