Typhoons, a kind of devastating natural disaster, have caused incalculable damages worldwide. The meteorological radar image is essential for weather forecasting, especially typhoons. The weather nowcasting (future 0–6 h) can be implemented via extrapolating radar images without using the primary weather forecasting method—the numerical weather prediction model. However, the existing related techniques based on statistics or artificial intelligence were not efficient enough. In this article, a novel radar image extrapolation algorithm named dynamic multiscale fusion-generative adversarial network (DMSF-GAN) was proposed. DMSF-GAN captures the future radar image distribution based on current radar images through modifying the GAN. In the generative module of GAN, an auto-encoder consisting of dynamic inception-3-D and feature connection blocks extracts significant features from current radar images. The feasibility of the proposed model was verified on a real radar image dataset, and the experimental results proved that the proposed algorithm could effectively capture the location and pattern of the future radar echo, especially for typhoon weather systems. Compared with the mainstream methods of radar image extrapolation such as optical-flow and recurrent neural network (RNN)-based models, DMSF-GAN has a more superior and robust performance, which is also suitable for running on low-configuration machines.