With a growing number of alternative Internet of Things (IoT) services that provide the same functionalities, Quality-of-Service (QoS) prediction has become an important research issue. Conventional central methods require that the historical QoS data is centralized. While the QoS data may be distributed in different edge servers. Due to privacy, these edge servers may not be willing to share their data with others for a better model representation. Besides, as each edge server is in charge of the collecting QoS data from the users in a specific area, the QoS data are likely to be heterogeneous. In this article, we propose a personalized federated tensor factorization framework for distributed privacy-preserving IoT services QoS prediction. We first adopt tensors to represent the QoS data with multidimensions and initialize a personalized model for each edge server. Then, each edge server performs local tensor factorization and exchanges the public component with a parameter master. By constraining the consistency of the global public component and the local personalized public components, the global model can learn information from edge servers during the training process. In addition, we conduct extensive experiments on a real-world QoS data set, the experimental results demonstrate that the proposed framework is efficient and effective.