With increasing concerns and regulations on data privacy, fine-tuning pretrained language models (PLMs) in federated learning (FL) has become a common paradigm for NLP tasks. Despite being extensively studied, the existing methods for this problem still face two primary challenges. First, the huge number of parameters in large-scale PLMs leads to excessive communication and computational overhead. Second, the heterogeneity of data and tasks across clients poses a significant obstacle to achieving the desired fine-tuning performance. To address the above problems, we propose FedMCP, a novel parameter-efficient fine-tuning method with model-contrastive personalization for FL. Specifically, FedMCP adds two lightweight adapter modules, i.e., the global adapter and the private adapter, to the frozen PLMs within clients. In a communication round, each client sends only the global adapter to the server for federated aggregation. Furthermore, FedMCP introduces a model-contrastive regularization term between the two adapters. This, on the one hand, encourages the global adapter to assimilate universal knowledge and, on the other hand, the private adapter to capture client-specific knowledge. By leveraging both adapters, FedMCP can effectively provide fine-tuned personalized models tailored to individual clients. Extensive experiments on highly heterogeneous cross-task, cross-silo datasets show that FedMCP achieves substantial performance improvements over state-of-the-art FL fine-tuning approaches for PLMs.