Most fusion methods tend to prioritize the subjective fusion effect, ignoring follow-up missions like segmentation or detection. Meanwhile, most of the feature extraction structures of fusion methods only use CNN to extract feature of images, which causes inadequate feature extraction thus making the fused images perform badly in follow-up missions. To make above issues addressed, we propose a fusion method via global-local feature extraction and edge-gradient preservation named GLEGNet. The global and local feature extraction module (GLEM) of GLEGNet is proposed to extract both global and local features, so as to refrain from losing key information for the final fusion. The edge and gradient preservation module(EGPM) is used to promote targets in fused images to have clear edges and gradient preservation to facilitate downstream tasks. The experiment results of comparison suggest the method we propose not only performs excellently in qualitative and quantitative comparisons, but also in follow-up missions and generalization experiments.