The wide exploitation of the theory of mobile communication and big data has enabled the flourishment of the outsourced system, where resource-constrained local users delegate batch of files and time-consuming evaluation tasks to the cloud server for outsourced storage and outsourced computation. Unfortunately, one single cloud server tends to become the target of comprise attack and bring about huge delay in response to the multi-user and multi-task setting where large quantity of inputs and outputs are respectively fed to and derived from the function evaluation, owing to its long distance from local users. To address this bottleneck of outsourced system, edge computing emerges that several edge nodes located between the cloud server and users collaborate to fulfill the tasks of outsourced storage and outsourced computation, meeting the real-time requirement but incurring new challenging issues of security and privacy-preserving. This paper firstly introduces the unique network architecture and security model of edge computing. Then, the state-of-the-art works in the field of privacy preserving of edge computing are elaborated, classified, and summarized based on the cryptographic techniques of data perturbation, fully homomorphic encryption, secure multiparty computation, fully homomorphic data encapsulation mechanism and verifiability and accountability in the following three phases: privacy-preserving data aggregation, privacy-preserving outsourced computation and their applications including private set intersection, privacy-preserving machine learning, privacy-preserving image processing, biometric authentication and secure encrypted search. Finally, several open research problems in privacy-preserving edge computing are discussed with convincing solutions, which casts light on its development and applications in the future.