High-quality and high-fidelity removal of noise in the Electrocardiogram (ECG) signal is of great significance to the auxiliary diagnosis of ECG diseases. In view of the single function of traditional denoising methods and the insufficient performance of signal details after denoising, a new method of ECG denoising based on the combination of the Generative Adversarial Network (GAN) and Residual Network is proposed. The method adopted in this paper is based on the GAN structure, and it restructures the generator and discriminator. In the generator network, residual blocks and Skip-Connecting are used to deepen the network structure and better capture the in-depth information in the ECG signal. In the discriminator network, the ResNet framework is used. In order to optimize the noise reduction process and solve the lack of local relevance considering the global ECG problem, the differential function and overall function of the maximum local difference are added in the loss function in this paper. The experimental results prove that the method used in this article has better performance than the current excellent S-Transform (S-T) algorithm, Wavelet Transform (WT) algorithm, Stacked Denoising Autoencoder (S-DAE) algorithm, and Improved Denoising Autoencoder (I-DAE) algorithm. Experiments show that the Root Mean Square Error (RMSE) of this method in the Massachusetts Institute of Technology and Beth Israel Hospital (MIT-BIH) noise pressure database is 0.0102, and the Signal-to-Noise Ratio (SNR) is 40.8526 dB, which is compared with that of the most advanced experimental methods. Our method improves the SNR by 88.57% on average. Besides the three noise intensities for comparison experiments, additional noise reduction experiments are also performed under four noise intensities in our paper. The experimental results verify the scientific nature of the model, which is that our method can effectively retain the important information conveyed by the original signal.