Pansharpening is a process of acquiring a multi-spectral image with high spatial resolution by fusing a low resolution multi-spectral image with a corresponding high resolution panchromatic image. In this paper, a new pansharpening method based on the Bayesian theory is proposed. The algorithm is mainly based on three assumptions: 1) the geometric information contained in the pan-sharpened image is coincident with that contained in the panchromatic image; 2) the pan-sharpened image and the original multi-spectral image should share the same spectral information; and 3) in each pan-sharpened image channel, the neighboring pixels not around the edges are similar. We build our posterior probability model according to above-mentioned assumptions and solve it by the alternating direction method of multipliers. The experiments at reduced and full resolution show that the proposed method outperforms the other state-of-the-art pansharpening methods. Besides, we verify that the new algorithm is effective in preserving spectral and spatial information with high reliability. Further experiments also show that the proposed method can be successfully extended to hyper-spectral image fusion.