Personalized federated learning is proposed to handle the data heterogeneity problem amongst clients by learning dedicated tailored local models for each user. However, existing works are often built in a centralized way, leading to high communication pressure and high vulnerability when a failure or an attack on the central server occurs. In this work, we propose a novel personalized federated learning framework in a decentralized (peer-to-peer) communication protocol named DisPFL, which employs personalized sparse masks to customize sparse local models on the edge. To further save the communication and computation cost, we propose a decentralized sparse training technique, which means that each local model in DisPFL only maintains a fixed number of active parameters throughout the whole local training and peer-to-peer communication process. Comprehensive experiments demonstrate that DisPFL significantly saves the communication bottleneck for the busiest node among all clients and, at the same time, achieves higher model accuracy with less computation cost and communication rounds. Furthermore, we demonstrate that our method can easily adapt to heterogeneous local clients with varying computation complexities and achieves better personalized performances.