Short-term rainfall nowcasting plays a crucial role in climate change adaptation, environmental protection, and sustainable economic development. The use of the Z-R relationship to convert radar reflectivity (Z) into rainfall rate (mm/h) enables timely warnings of hazardous weather events such as flash floods, landslides, and storms. However, deep learning models such as CNN-GRU and ConvLSTM, ConvGRU still face limitations due to their insufficient ability to capture temporal dependencies, resulting in suboptimal performance in nowcasting extreme rainfall events. To address these shortcomings, this paper proposes S2R-GAN, a novel frame-work based on Generative Adversarial Networks (GANs) for radar image nowcasting within a one-hour time horizon. The model incorporates a generator utilizing a CNN-GRU architecture to learn spatiotemporal sequences, integrated with a UNet structure to reconstruct high-resolution image details. In addition, several enhancements are introduced to further improve nowcasting accuracy. Experimental results on radar reflectivity images collected from the Phadin station demonstrate that S2R-GAN significantly outperforms the baseline CNN-GRU and Rad-cGAN models. S2R-GAN outperforms all other models, reducing MSE by 35.29%, MAE by 45.45%, and RMSE by 31.84% compared to Rad-cGAN (the best-performing model among the compared baselines). Overall, S2R-GAN not only improves nowcasting performance but also demonstrates strong potential for integration into operational weather nowcasting systems.