Remote sensing image fusion, an effective method that integrates information contained in multispectral and panchromatic images, has become a powerful application technology in fields such as territorial spatial planning and disaster detection. A new method of remote sensing image fusion in non-subsampling shearlet transform (NSST) domain is proposed on the basis of research on fusion strategy in the NSST domain. First, the source image is NSST decomposed into low-frequency coefficients and multi-directional high-frequency subbands. Subsequently, to solve the problems of energy conservation and detail extraction, an image feature weighting mechanism based on the mean spectral radius weights the energy attribute and the improved Laplacian energy sum and applies these to low-frequency coefficient fusion. Next, an improved dual-channel pulse coupled neural network is developed to fuse the high-frequency subbands by combining the weighted adaptive method with the direction information to determine the weight. Finally, the fused low-frequency coefficients and high-frequency subbands are used for reconstruction to obtain the fused image. The effectiveness of this method is verified by 48 sets of satellite images with three different resolutions, namely, GF-2, GeoEye, and WorldView-3. The comparison experiment with five fusion methods shows this new method can achieve good results in visual perception and quantitative evaluation indicators.