Remote-sensing images typically present multiple scene categories, significant intraclass variance, and high interclass similarity. Conventional deep networks such as convolutional neural networks (CNNs) can neither adequately represent the features of target objects nor accurately distinguish between object and background information in remote-sensing scene images. Moreover, these networks typically exhibit large parameter sizes, thus resulting in low classification accuracy and inefficient training. Hence, a resistive CNN that can perform remote-sensing scene classification is proposed. A context-aware enhanced transformer module was introduced to fuse shared weights and context-aware weights for capturing both high- and low-frequency features. A multiscale selective kernel (SK) unit building block was integrated into the convolution block, and different convolution kernels were selected based on feature maps of different levels. Additionally, feature information of different scales was extracted to improve the processing ability of the model for complex scenes. Furthermore, a low-power and high-speed resistive CNN was constructed by weight mapping resistor crossbar arrays, thus reducing the computational overhead. Experimental results on the publicly available UCMercedLandUse dataset with 21 classes and the NWPU-RESISC45 dataset with 45 classes indicate classification accuracies of 94.76% and 87.54%, respectively. These accuracies represent improvements of 5.95 percentage points and 5.07 percentage points, respectively, compared with baseline models in addition to significantly reduced model parameters. The accuracy losses of the improved resistive CNN model on the two abovementioned datasets are only 0.24 percentage points and 0.23 percentage points, respectively. Thus, it is a promising model for promoting the advancement of edge computing.