Accurate weather prediction is essential for many aspects of life, notably the early warning of extreme weather events such as rainstorms. Short-term predictions of these events rely on forecasts from numerical weather models, in which, despite much improvement in the past decades, outstanding issues remain concerning model uncertainties, and increasing demands for computation and storage resources. In recent years, the advance of deep learning offers a viable alternative approach. Here, we show that a 3D convolutional neural network using a single frame of meteorology fields as input is capable of predicting the precipitation spatial distribution. The network is developed based on 39-years (1980-2018) data of meteorology and daily precipitation over the contiguous United States. The results bring fundamental advancements in weather prediction. First, the trained network alone outperforms the state-of-the-art weather models in predicting daily total precipitation, and the superiority of the network extends to forecast leads up to 5 days. Second, combining the network predictions with the weather-model forecasts significantly improves the accuracy of model forecasts, especially for heavy-precipitation events. Third, the millisecond-scale inference time of the network facilitates large ensemble predictions for further accuracy improvement. These findings strongly support the use of deep-learning in short-term weather predictions.