Quantitative precipitation forecasting in numerical weather prediction (NWP) models rely on physical parameterization schemes. However, these schemes involve considerable uncertainties due to limited knowledge of the mechanisms involved in the precipitating process, ultimately leading to degraded precipitation forecasting skills. To address this issue, our study proposes using a Swin-Transformer based deep learning (DL) model to quantitatively map fundamental variables solved by NWP models to precipitation maps. Our results show that the DL model effectively extracts features over meteorological variables, leading to improved precipitation skill scores of 21.7%, 60.5%, and 45.5% for light rain, moderate rain, and heavy rain, respectively, on an hourly basis. We also evaluate two case studies under different driven synoptic conditions and show promising results in estimating heavy precipitation during strong convective precipitation events. Overall, the proposed DL model can provide a vital reference for capturing precipitation-triggering mechanisms and enhancing precipitation forecasting skills. Additionally, we discuss the sensitivities of the fundamental meteorological variables used in this study, training strategies, and performance limitations.