Remote sensing image fusion can effectively solve the inherent contradiction between spatial resolution and spectral resolution of imaging systems. At present, the fusion methods of remote sensing images based on multi-scale transform usually set fusion rules according to local feature information and pulse-coupled neural network (PCNN), but there are problems such as single local feature, as fusion rule cannot effectively extract feature information, PCNN parameter setting is complex, and spatial correlation is poor. To this end, a fusion method of remote sensing images that combines low-level visual features and a parameter-adaptive dual-channel pulse-coupled neural network (PADCPCNN) in a non-subsampled shearlet transform (NSST) domain is proposed in this paper. In the low-frequency sub-band fusion process, a low-level visual feature fusion rule is constructed by combining three local features, local phase congruency, local abrupt measure, and local energy information to enhance the extraction ability of feature information. In the process of high-frequency sub-band fusion, the structure and parameters of the dual-channel pulse-coupled neural network (DCPCNN) are optimized, including: (1) the multi-scale morphological gradient is used as an external stimulus to enhance the spatial correlation of DCPCNN; and (2) implement parameter-adaptive representation according to the difference box-counting, the Otsu threshold, and the image intensity to solve the complexity of parameter setting. Five sets of remote sensing image data of different satellite platforms and ground objects are selected for experiments. The proposed method is compared with 16 other methods and evaluated from qualitative and quantitative aspects. The experimental results show that, compared with the average value of the sub-optimal method in the five sets of data, the proposed method is optimized by 0.006, 0.009, 0.009, 0.035, 0.037, 0.042, and 0.020, respectively, in the seven evaluation indexes of information entropy, mutual information, average gradient, spatial frequency, spectral distortion, ERGAS, and visual information fidelity, indicating that the proposed method has the best fusion effect.