Hyperspectral imaging is widely used in many fields such as geology, medicine, meteorology, and so on. Despite the high spectral resolution, the spatial resolution of the hyperspectral sensors is severely limited. In this paper, we propose a novel maximum a posteriori (MAP)-based approach based on the joint superresolution of the abundance maps, to enhance the resolution of hyperspectral images. In the proposed approach, first, the endmembers and their abundance maps are estimated using Vertex Component Analysis (VCA) and Fully Constrained Least Squares (FCLS), respectively. Second, a high resolution (HR) abundance map is reconstructed for each low resolution (LR) abundance map using a MAP based approach. In the MAP-formulation data, smoothness and edge preservation constraints are extended to include a unity constraint term specific to abundances. Finally, HR hyperspectral images are reconstructed using the HR abundance maps. The proposed algorithm is tested on both synthetic images and real image sequences. The experimental results and comparative analysis verify the effectiveness of the proposed algorithm.