Recently, deep-learning weather forecasting models have surpassed traditional numerical models in terms of the accuracy of meteorological variables. However, there is considerable potential for improvements in precipitation forecasts, especially for heavy precipitation events. To address this deficiency, we propose Leadsee-Precip, a global deep learning model to generate precipitation from meteorological circulation fields. The model utilizes an information balance scheme to tackle the challenges of predicting heavy precipitation caused by the long-tail distribution of precipitation data. Additionally, more accurate satellite and radar-based precipitation retrievals are used as training targets. Compared to artificial intelligence global weather models, the heavy precipitation from Leadsee-Precip is more consistent with observations and shows competitive performance against global numerical weather prediction models. Leadsee-Precip can be integrated with any global circulation model to generate precipitation forecasts. But the deviations between the predicted and the ground-truth circulation fields may lead to a weakened precipitation forecast, which could potentially be mitigated by further fine-tuning based on the predicted circulation fields.