The deep-learning-based image super-resolution opens a new direction for the remote sensing field to reconstruct further information and details from captured images. However, most current SR works try to improve the performance by increasing the complexity of the model, which results in significant computational costs and memory consumption. In this paper, we propose a lightweight model named pixel-wise attention residual network for optical remote sensor images, which can effectively solve the super-resolution task of multi-satellite images. The proposed method consists of three modules: the feature extraction module, feature fusion module, and feature mapping module. First, the feature extraction module is responsible for extracting the deep features from the input spatial bands with different spatial resolutions. Second, the feature fusion module with the pixel-wise attention mechanism generates weight coefficients for each pixel on the feature map and fully fuses the deep feature information. Third, the feature mapping module is aimed to maintain the fidelity of the spectrum by adding the fused residual feature map directly to the up-sampled low-resolution images. Compared with existing deep-learning-based methods, the major advantage of our method is that for the first time, the pixel-wise attention mechanism is incorporated in the task of super-resolution fusion of remote sensing images, which effectively improved the performance of the fusion network. The accuracy assessment results show that our method achieved superior performance of the root mean square error, signal-to–reconstruction ratio error, universal image quality index, and peak signal noise ratio compared to competing approaches. The improvements in the signal-to-reconstruction ratio error and peak signal noise ratio are significant, with a respective increase of 0.15 and 0.629 dB for Sentinel-2 data, and 0.196 and 1 dB for Landsat data.