Fairness has emerged as one of the key challenges in federated learning. In horizontal federated settings, data heterogeneity often leads to substantial performance disparities across clients, raising concerns about equitable model behavior. To address this issue, we propose FedGA, a fairness-aware federated learning algorithm. We first employ the Gini coefficient to measure the performance disparity among clients. Based on this, we establish a relationship between the Gini coefficient $G$ and the update scale of the global model ${U_s}$, and use this relationship to adaptively determine the timing of fairness intervention. Subsequently, we dynamically adjust the aggregation weights according to the system's real-time fairness status, enabling the global model to better incorporate information from clients with relatively poor performance.We conduct extensive experiments on the Office-Caltech-10, CIFAR-10, and Synthetic datasets. The results show that FedGA effectively improves fairness metrics such as variance and the Gini coefficient, while maintaining strong overall performance, demonstrating the effectiveness of our approach.