Human Activity Recognition (HAR) plays a significant role in recent years due to its applications in various fields including health care and well-being. Traditional centralized methods reach very high recognition rates, but they incur privacy and scalability issues. Federated learning (FL) is a leading distributed machine learning (ML) paradigm, to train a global model collaboratively on distributed data in a privacy-preserving manner. However, for HAR scenarios, the existing action recognition system mainly focuses on a unified model, i.e. it does not provide users with personalized recognition of activities. Furthermore, the heterogeneity of data across user devices can lead to degraded performance of traditional FL models in the smart applications such as personalized health care. To this end, we propose a novel federated learning model that tries to cope with a statistically heterogeneous federated learning environment by introducing a group-personalized FL (GP-FL) solution. The proposed GP-FL algorithm builds several global ML models, each one trained iteratively on a dynamic group of clients with homogeneous class probability estimations. The performance of the proposed FL scheme is studied and evaluated on real-world HAR data. The evaluation results demonstrate that our approach has advantages in terms of model performance and convergence speed with respect to two baseline FL algorithms used for comparison. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.