Heavy precipitation from tropical cyclones (TCs) may result in disasters, such as floods and landslides, leading to substantial economic damage and loss of life. Prediction of TC precipitation based on ensemble post-processing procedures using machine learning (ML) approaches has received considerable attention for its flexibility in modeling and its computational power in managing complex models. However, when applying ML techniques to TC precipitation for a specific area, the available observation data are typically insufficient for comprehensive training, validation, and testing of the ML model, primarily due to the rapid movement of TCs. We propose to use the convolutional neural network (CNN) as a deep ML model to leverage the spatial information of precipitation. The proposed model has three distinct features that differentiate it from traditional CNNs applied in meteorology. First, it utilizes data augmentation to alleviate challenges posed by the small sample size. Second, it contains geographical and dynamic variables to account for area-specific features and the relative distance between the study area and the moving TC. Third, it applies unequal weights to accommodate the temporal structure in the training data when calculating the objective function. The proposed CNN-all model is then illustrated with the TC Soudelor's impact on Taiwan. Soudelor was the strongest TC of the 2015 Pacific typhoon season. The results show that the inclusion of augmented data and dynamic variables improves the prediction of heavy precipitation. The proposed CNN-all outperforms traditional CNN models, based on the continuous probability skill score (CRPSS), probability plots, and reliability diagram. The proposed model has the potential to be utilized in a wide range of meteorological studies.