Precipitation nowcasting is an important task in weather forecast. The key challenge of the task lies at radar echo map extrapolation. Recent studies show that a convolutional recurrent neural network (ConvRNN) is a promising direction to solve the problem. However, the extrapolation results of the existing ConvRNN methods tend to be blurring and unrealistic. Recent studies show that generative adversarial network (GAN) is a promising tool to address the drawback, while it suffers from the instability for training. In this letter, we build a novel ConvRNN model based on the energy-based GAN for radar echo map extrapolation. The method can alleviate the blurring and unrealistic issues and is more stable. We have conducted experiments on a real-world data set, and the results show that the proposed method outperforms several existing models, including optical flow, convolution gated recurrent unit (ConvGRU), and generative adversarial ConvGRU (GA-ConvGRU).