Federated learning (FL) is an emerging machine learning paradigm in which a central server coordinates multiple participants (a.k.a. FL clients) to train a model collaboratively on decentralized data with privacy protection. This paradigm constrains that all clients have to train models with the same structures (homogeneous). In practice, FL often faces statistical heterogeneity, system heterogeneity and model heterogeneity challenges. These challenging issues inspire the field of Model-Heterogeneous Personalized Federated Learning (MHPFL) which aims to train a personalized and heterogeneous local model for each FL client. Existing MHPFL approaches cannot achieve satisfactory model performance, acceptable computational overhead and efficient communication simultaneously. To bridge this gap, we propose a novel computation- and communication-efficient model-heterogeneous personalized Federated learning framework based on LoRA tuning (FedLoRA). It is designed to incorporate a homogeneous small adapter for each client's heterogeneous local model. Both models are trained following the proposed iterative training for global-local knowledge exchange. The homogeneous small local adapters are sent to the FL server to be aggregated into a global adapter. In this way, FL clients can train heterogeneous local models without incurring high computation and communication costs. We theoretically prove the non-convex convergence rate of FedLoRA. Extensive experiments on two real-world datasets demonstrate that FedLoRA outperforms six state-of-the-art baselines, beating the best approach by 1.35% in terms of test accuracy, 11.81 times computation overhead reduction and 7.41 times communication cost saving.