Nowcasting of convective storms is urgently needed yet rather challenging. Current nowcasting methods are mostly based on radar echo extrapolation, which suffer from the insufficiency of input information and ineffectiveness of model architecture. A novel deep‐learning (DL) model, FURENet, is designed for extracting information from multiple input variables to make predictions. Polarimetric radar variables, KDP and ZDR, which provide extra microphysics and dynamic structure information of storms, are fed into the model to improve nowcasting. Two representative cases indicate that KDP and ZDR can help the DL model better forecast convective organization and initiation. Quantitative statistical evaluation shows using FURENet, KDP, and ZDR synergistically improve nowcasting skills (CSI score) by 13.2% and 17.4% for the lead time of 30 and 60 min, respectively. Further evaluation shows the microphysical information provided by the polarimetric variables can enhance the DL model in understanding the evolution of convective storms and making more trustable nowcasts. Plain Language Summary Severe convective precipitation is a major cause of many hazards. However, very short‐term forecasting, i.e., nowcasting, of convective precipitation is rather challenging. Current nowcasting methods suffer from insufficiency of physics information of input data and ineffectiveness of model architecture. As an advanced observing tool, polarimetric weather radar can provide crucial microphysics and dynamic structure information of convective precipitation systems. To incorporate polarimetric radar variables into the nowcasting task, this study proposes a novel model architecture termed FURENet based on deep learning. FURENet uses U‐Net as a flexible backbone, and is specially designed to facilitate exploiting information from multiple input variables. By training the model with polarimetric radar variables (KDP and ZDR) as input, significant improvement of forecasting the initiation, development and evolution of convective storms is achieved. The results also show the effectiveness of model architecture. Key Points A deep‐learning approach termed FURENet is proposed for convective precipitation nowcasting with multiple input variables Polarimetric radar variables are used to provide microphysics and dynamic structure information of convective storms in the model Experiments with FURENet show significant improvement on nowcasting performance