Image fusion aims to integrate the significant information from multimodal images to obtain a single image. In this article, a fractional-order variation with convolution norm is proposed for infrared and visible image fusion (IVIF). In our model, a convolution norm ${l}_{\otimes }$ is developed for infrared and visible fidelity terms, which can provide the structural group sparseness, alleviating the residual offset. Moreover, the fractional-order variation is employed instead of total variation (TV), preserving more details and avoiding the staircase effect. Simultaneously, a focused term is utilized to prevent the luminance degradation of the fused result. Finally, extensive experiments are performed on public datasets. The results exhibit that the proposed method achieves better performance in subjective and objective evaluation compared with the excellent methods.