Cloud service mode has obtained broad application space with the rapid development of cloud computing technology. Such mode has provided users with incomparable computing power and storage space. However, privacy security of users is a primary problem in the promotion and application of the service mode. How to guarantee both the privacy and availability of data in the process of data computation remains a major challenge, and as a key means to solve this problem, homomorphic encryption technique has been a hot subject in international and domestic academic circles in recent years. In this paper, the privacy security of cloud computing, the research progress of homomorphic encryption and the application of homomorphic encryption technique in privacy protection of cloud computing are introduced. Analysis of advantages and disadvantages of various homomorphic encryption schemes is emphasized, and the future research direction is proposed.