In this paper we propose a Group-Sparse Representation based method with applications to Face Recognition (GSR-FR). The novel sparse representation variational model includes a non-convex sparsity-inducing penalty and a robust non-convex loss function. The penalty encourages group sparsity by using approximation of the ℓ0-quasinorm, and the loss function is chosen to make the algorithm robust to noise, occlusions and disguises. The solution of the non-trivial non-convex optimization problem is efficiently obtained by a majorization-minimization strategy combined with forward-backward splitting, which in particular reduces the solution to a sequence of easier convex optimization sub-problems. Extensive experiments on widely used face databases show the potentiality of the proposed model and demonstrate that the GSR-FR algorithm is competitive with state-of-the-art methods based on sparse representation, especially for very low dimensional feature spaces.