Face identification and resolution technology is crucial to ensure the identity consistency of humans in physical space and cyber space. In the current Internet of Things (IoT) and big data situation, the increase of applications based on face identification and resolution raises the demands of computation, communication, and storage capabilities. Therefore, we have proposed the fog computing-based face identification and resolution framework to improve processing capacity and save the bandwidth. However, there are some security and privacy issues brought by the properties of fog computing-based framework. In this paper, we propose a security and privacy preservation scheme to solve the above issues. We give an outline of the fog computing-based face identification and resolution framework, and summarize the security and privacy issues. Then the authentication and session key agreement scheme, data encryption scheme, and data integrity checking scheme are proposed to solve the issues of confidentiality, integrity, and availability in the processes of face identification and face resolution. Finally, we implement a prototype system to evaluate the influence of security scheme on system performance. Meanwhile, we also evaluate and analyze the security properties of proposed scheme from the viewpoint of logical formal proof and the confidentiality, integrity, and availability (CIA) properties of information security. The results indicate that the proposed scheme can effectively meet the requirements for security and privacy preservation.