Federated learning is a distributed machine learning approach that enables model delivery and aggregation without compromising the privacy and security of local data. However, federated learning faces a major challenge: the large size of the models and the parameters that need to be communicated multiple times between the client and the server, bringing difficulties for small devices with insufficient communication capability. Therefore, this study set up the client and server to communicate with each other only once. Another challenge in federated learning is the data imbalance among different clients. The model aggregation for servers becomes inefficient in data imbalance. To overcome these challenges, the study proposes a lightweight federated learning framework that requires only one-shot communication between the client and the server. The framework also introduces an aggregation policy algorithm, FBL-LD. The algorithm selects the most reliable and dominant model from the client models in a one-shot communication and adjusts the weights of other models based on a validation set to achieve a generalized federated model. FBL-LD reduces the communication overhead and improves aggregation efficiency. Experimental results show that FBL-LD outperforms existing federated learning algorithms in terms of accuracy and robustness to data imbalance.