Nowadays, medical image fusion serves as a significant aid for the precise diagnosis or surgical navigation. In this paper, we propose a novel tensor factorization based fusion strategy which well combines the multimodal, multiscale nature of medical images and multiway structure of tensors. Since our model adopts the sparse representation (SR) prior, we suffer from the systematic underestimation of the true solution because of the L1-norm regularization term. To address this problem, we introduce the generalized minimax-concave (GMC) penalty into our framework, which is a non-convex regularization term itself. It is beneficial for the whole cost function to maintain convexity. Furthermore, we combine the alternating direction method of multipliers (ADMM) algorithm and forward-backward (FB) method to achieve the optimization process. We conduct extensive experiments on five kinds of practical medical image fusion problems with 96 pairs of images in total. The results confirm that our model has great improvements in visual performance and objective metrics against the existing methods.