In the field of precipitation nowcasting, the existing radar echo extrapolation methods based on deep learning have some shortcomings. In terms of image quality, the prediction images are indistinct and deficient in small-scale details, while in terms of prediction accuracy, the precipitation results are not accurate enough. This study proposes a multi-scale generative adversarial (MCGAN) model, which consists of a multi-scale convolutional generator and a fully convolutional discriminator. The generator part adopts an encoder-decoder architecture, which mainly includes multi-scale convolutional blocks and downsampling gating units. Using the dynamic spatiotemporal variability loss function, the MCGAN model is trained under the generative adversarial network (GAN) framework to achieve more accurate and clearer predictions of echo intensity and distribution. Verified in the Shanghai public radar dataset, the performance of the model in this study decreases by 11.15% in the MSE index in image quality evaluation, and increases by 8.99% and 2.95% in the SSIM index and PSNR index compared with the mainstream deep learning models, respectively. In the evaluation of prediction accuracy, the CSI, POD, and HSS indexes increase by 11.92%, 15.89%, and 9.01% on average, and the FAR index decreases by 14.81% on average. In addition, the role of each component of the MCGAN model is demonstrated by ablation experiments.