Text summarization is essential for information aggregation and demands large amounts of training data. However, concerns about data privacy and security limit data collection and model training. To eliminate this concern, we propose a federated learning text summarization scheme, which allows users to share the global model in a cooperative learning manner without sharing raw data. Personalized federated learning (PFL) balances personalization and generalization in the process of optimizing the global model, to guide the training of local models. However, multiple local data have different distributions of semantics and context, which may cause the local model to learn deviated semantic and context information. In this paper, we propose FedSUMM, a dynamic gradient adapter to provide more appropriate local parameters for local model. Simultaneously, FedSUMM uses differential privacy to prevent parameter leakage during distributed training. Experimental evidence verifies FedSUMM can achieve faster model convergence on PFL algorithm for task-specific text summarization, and the method achieves superior performance for different optimization metrics for text summarization.