Abstract: At present, the remote sensing image fusion algorithm cannot improve the spatial quality and spectral fidelity of the multispectral image simultaneously. A variational image fusion algorithm based on spatial and spectral constraints is proposed to solve this problem. Firstly, the difference of each band before and after fusion and the difference of the observed spatial quality are assumed to be consistent. Based on the assumption, the edge-based spatial information constraint is proposed. And then on the assumption that the correlation of bands remains unchanged before and after the fusion, the spectral-band-ratio-based spectral information constraint is proposed. Finally, these two constraints are integrated into the variational model, which is minimized by a gradient descent method. Experiments using Pleiades and Quick Bird data sets and more comparison with state-of-the-art algorithms show that our fusion images are more prominent and better on spatial detail and spectral fidelity than other state-of-the-art algorithms.