Federated Learning (FL) is an innovative machine learning approach that facilitates collaborative model training across distributed devices while safeguarding individual data privacy. However, traditional FL algorithms encounter challenges of model instability in practice, stemming from issues such as uneven data distribution and client heterogeneity. To address these challenges, this study proposes a FL algorithm based on Bhattacharyya regularization (FedBC). The algorithm effectively improves the consistency of models among local clients, and demonstrates promising results in handling the heterogeneity of non-independent identically distributed (non-iid) data in FL. Experimental results show that the proposed algorithm achieves excellent convergence speed and model performance, significantly enhancing the efficiency and robustness of FL while preserving data privacy.