This paper studies a fast multi-band image fusion algorithm for high-spatial low-spectral resolution and low-spatial high-spectral resolution images. The popular forward model and the conventional Gaussian prior are used to form the posterior of the target image. Maximizing the posterior leads to solving a matrix Sylvester equation. By exploiting the properties of the circulant and decimation matrices associated with the fusion problem, a closed-form solution for the corresponding Sylvester equation is obtained, avoiding any iterative update step. Simulation results show that the proposed approach using this closed-form solution achieves the same performance as existing algorithms with the advantage of significantly decreasing the computational complexity of these algorithms.