Severe convective weather, characterized by short-term intense precipitation, thunderstorms, and strong winds, poses significant threats to human life and property. Therefore, accurate and efficient prediction of severe convective weather is crucial for disaster prevention. Currently, utilizing deep learning for radar echo extrapolation stands as the primary method for forecasting severe convective weather. We propose a predictive recurrent neural network model that integrates a self-attention mechanism, specifically designed for radar echo extrapolation in severe convective weather forecasting. The self-attention mechanism offers the advantage of being lightweight, as it does not substantially increase the model parameters. Additionally, it facilitates global attention extraction, thereby enhancing the model's accuracy to some extent. By utilizing radar echo images from the previous hour as input, the model undergoes self-learning to achieve the best forecast for radar echo extrapolation in the subsequent two hours. Research findings demonstrate that our model outperforms other models in accurately predicting severe convective weather within this two-hour timeframe.