This paper presents a multiband image fusion algo- rithm based on unsupervised spectral unmixing for combining a high-spatial–low-spectral-resolution image and a low-spatial– high-spectral-resolution image. The widely used linear observa- tion model (with additive Gaussian noise) is combined with the linear spectral mixture model to form the likelihoods of the obser- vations. The nonnegativity and sum-to-one constraints resulting from the intrinsic physical properties of the abundances are intro- duced as prior information to regularize this ill-posed problem. The joint fusion and unmixing problem is then formulated as maximizing the joint posterior distribution with respect to the endmember signatures and abundance maps. This optimization problem is attacked with an alternating optimization strategy. The two resulting subproblems are convex and are solved efficiently using the alternating direction method of multipliers. Experiments are conducted for both synthetic and semi-real data. Simulation results show that the proposed unmixing-based fusion scheme im- proves both the abundance and endmember estimation compared with the state-of-the-art joint fusion and unmixing algorithms.