Nowcasting is an important technique for weather forecasting because sudden weather changes significantly affect human life. The encoding-forecasting model, which is a state-of-the-art architecture in the field of data-driven radar extrapolation, does not particularly focus on the latest data when forecasting natural phenomena. This paper proposes a weighted broadcasting method that emphasizes the latest data of the time step to improve the nowcasting performance. This weighted broadcasting method allows the most recent rainfall patterns to have a greater impact on the forecasting network by extending the architecture of the existing encoding-forecasting model. Experimental results show that the proposed model is 1.74% and 2.20% better than the existing encoding-forecasting model in terms of mean absolute error and critical success index, respectively. In the case of heavy rainfall with an intensity of 30 mm/h or higher, the proposed model was more than 30% superior to the existing encoding-forecasting model. Therefore, applying the weighted broadcasting method, which explicitly places a high emphasis on the latest information, to the encoding-forecasting model is considered as an improvement that is applicable to the state-of-the-art implementation of data-driven radar-based precipitation nowcasting.