We propose a novel privacy-preserving QoS forecasting approach - Edge-Laplace QoS (QoS forecasting with Laplace noise in mobile Edge environments). Edge-Laplace QoS is able to accurately and efficiently forecast Quality of Service (QoS) of various Web Services, while effectively protecting user privacy in mobile edge environments. We employ an improved differential privacy method to add dynamic disguises to the original QoS data in the edge environment to protect user data privacy. A collaborative filtering method is adopted to retrieve similar users' accessing records based on geographic locations of their accessed servers for QoS forecasting. We conduct a set of experiments using several public network data sets. The results show that the efficiency of Edge-Laplace QoS is superior to traditional forecasting approaches. Edge-Laplace QoS is also validated to be more suitable for edge environments than traditional privacy-preserving approaches.