As machine learning becomes increasingly incorporated in crucial decision-making scenarios such as healthcare, recruitment, and loan assessment, there have been increasing concerns about the privacy and fairness of such systems. Federated learning has been viewed as a promising solution for collaboratively learning machine learning models among multiple parties while maintaining the privacy of their local data. However, federated learning also poses new challenges in mitigating the potential bias against certain populations (e.g., demographic groups), which typically requires centralized access to the sensitive information (e.g., race, gender) of each data point. Motivated by the importance and challenges of group fairness in federated learning, in this work, we propose FairFed, a novel algorithm to enhance group fairness via a fairness-aware aggregation method, aiming to provide fair model performance across different sensitive groups (e.g., racial, gender groups) while maintaining high utility. The formulation can potentially provide more flexibility in the customized local debiasing strategies for each client. When running federated training on two widely investigated fairness datasets, Adult and COMPAS, our proposed method outperforms the state-of-the-art fair federated learning frameworks under a high heterogeneous sensitive attribute distribution.