In image fusion, most edge-preserving filters corrupt structure and texture information during the optimization process, and the noise will also seriously affect the fusion result, which may cause problems such as loss of details and textures in the fusion results. An infrared and visible image fusion method based on RPCA(Robust principal component analysis) algorithm is proposed in this paper, which can effectively improve figure definition and visual information fidelity. Firstly, infrared and visible light images were decomposed into low rank and sparse images through Robust principal component analysis. Then, relative total variation (RTV) and average energy method were adopted to process low rank and sparse images. Finally, the final fusion image was obtained by inverse NSCT transformation. The experimental results show that, compared with the other methods, the fusion image generated by the method proposed in this paper has certain improvements in the average gradient, spatial frequency, edge intensity and mutual information, with an increase of 10.6% to 72.6%, 15% to 60.2%, 9.7% to 69.6%, and 22.7% to 229.7%, respectively.