The key challenge of personalized federated learning (pFL) is to capture the statis tical heterogeneity properties of data with inexpensive communications and gain customized performance for devices. To address this, we introduced personalized multi-tier federated learning with Moreau envelopes (pFedMT) to obtain optimized and personalized local models when there are known cluster structures across devices. Moreau envelopes are used as the devices’ and teams’ regularized loss functions. We provide theoretical guarantees of pFedMT for both strongly convex and non-convex settings. pFedMT achieves linear convergence rates for strongly convex settings and sub-linear rates for non-convex and smooth settings.