As a popular signal modeling technique, sparse representation (SR) has achieved great success in image fusion over the last few years with a number of effective algorithms being proposed. However, due to the patch-based manner applied in sparse coding, most existing SR-based fusion methods suffer from two drawbacks, namely, limited ability in detail preservation and high sensitivity to misregistration, while these two issues are of great concern in image fusion. In this letter, we introduce a recently emerged signal decomposition model known as convolutional sparse representation (CSR) into image fusion to address this problem, which is motivated by the observation that the CSR model can effectively overcome the above two drawbacks. We propose a CSR-based image fusion framework, in which each source image is decomposed into a base layer and a detail layer, for multifocus image fusion and multimodal image fusion. Experimental results demonstrate that the proposed fusion methods clearly outperform the SR-based methods in terms of both objective assessment and visual quality.