The image resolutions of some channels of Fengyun-4A (FY-4A) satellite are low, which affects the ability of multi-channel collaborative monitoring of Fengyun satellites. To solve this problem, enhanced super-resolution generative adversarial networks (ESRGAN) algorithm is proposed to implement the super-resolution reconstruction of FY-4A images. Based on the generator architecture of ESRGAN, the transfer learning strategy is used, and the pre-training weight is taken as the initial value of the model in this method. A set of residual-in-residual dense blocks (RRDB) containing 5 hollow convolutional layers is designed, and the loss function is optimized. The results show that under the reconstruction of 4 times image resolution, compared with ESRGAN algorithm, the peak signal-to-noise ratio (PSNR), structural similarity (SSIM) and correlation coefficient (CC) of the improved ESRGAN algorithm increase by 0.704, 0.029 and 0.002 respectively, while root-mean-square error (RMSE) decreases by 10%. The reconstructed images are clearer and more natural, and the texture is more detailed.