The current hyperspectral and multi-spectral image fusion algorithms have such defects as having large solution space, not considering the physical meaning of hyperspectral data, and being prone to local optimal solutions.To solve these problems, a hyperspectral and multi-spectral image fusion algorithm is proposed based on Minimum Volume Constraint and Coupled Non-negative Matrix Factorization (MVC-CNMF).In the process of separating the mixed pixels, the algorithm takes the physical meaning of the image into consideration and adds the minimum volume constraint of the endmember single body.Simulation results show that the proposed algorithm can effectively overcome the defects in the existing fusion algorithms, accurately match the endmember with the abundance of hyperspectral and multi-spectral images, and obtain high-spatial-resolution fused images.This algorithm is especially suitable for the hyperspectral images with a large number of endmembers.