Reliable near-real-time precipitation estimation is crucial for scientific research and resistance to natural disasters such as floods. Compared with ground-based precipitation measurements, satellite-based precipitation measurements have great advantages, but precipitation estimation based on satellite is still a challenging issue. In this paper, we propose a deep learning model named Attention-Unet for precipitation estimation. The model utilizes the high temporal, spatial and spectral resolution data of the FY4A satellite to improve the accuracy of precipitation estimation. To evaluate the effectiveness of the proposed model, we compare it with operational near-real-time satellite-based precipitation products and deep learning models which proved to be effective in precipitation estimation. We use classification metrics such as Probability of detection (POD), False Alarm Ratio (FAR), Critical success index (CSI), and regression metrics including Root Mean Square Error (RMSE) and Pearson correlation coefficient (CC) to evaluate the performance of precipitation identification and precipitation amounts estimation, respectively. Furthermore, we select an extreme precipitation event to validate the generalization ability of our proposed model. Statistics and visualizations of the experimental results show the proposed model has better performance than operational precipitation products and baseline deep learning models in both precipitation identification and precipitation amounts estimation. Therefore, the proposed model has the potential to serve as a more accurate and reliable satellite-based precipitation estimation product. This study suggests that applying an appropriate deep learning algorithm may provide an opportunity to improve the quality of satellite-based precipitation products.