The increasing concern for data privacy has driven the rapid development of federated learning (FL), a privacy-preserving collaborative paradigm. However, the statistical heterogeneity among clients in FL results in inconsistent performance of the server model across various clients. Server model may show favoritism towards certain clients while performing poorly for others, heightening the challenge of fairness. In this paper, we reconsider the inconsistency in client performance distribution and introduce the concept of adversarial multi-armed bandit to optimize the proposed objective with explicit constraints on performance disparities. Practically, we propose a novel multi-armed bandit-based allocation FL algorithm (FedMABA) to mitigate performance unfairness among diverse clients with different data distributions. Extensive experiments, in different Non-I.I.D. scenarios, demonstrate the exceptional performance of FedMABA in enhancing fairness.