The sixth-generation (6G) mobile communication network is expected to provide world-connected smart and autonomous services by leveraging artificial intelligence (AI) technologies. In particular, federated learning (FL) is advocated to promote the implementations of ubiquitous AI applications in 6G, where massive distributed data is utilized to cooperatively train AI models as well as protect privacy and reduce resource consumption. However, due to the large number of interactions among mobile devices or infrastructures in FL, the AI inevitably suffers from a series of potential privacy and security risks. In this article, we investigate the security and privacy of AI-enabled 6G. Specifically, we first present the AI-enabled 6G architecture, including the space-air-ground-ocean integrated network (SAGOIN) architecture and two different FL-based AI model training frameworks in 6G. Furthermore, we discuss in detail the privacy and security threats, including cheating attack, low-quality local model training attack, and privacy stealing attack. Afterwards, we present a case study to design the security and privacy preservation scheme by integrating the trust evaluation, Q-learning based incentive, and local differential privacy (LDP) mechanism. Finally, we give out several future research directions in promising AI-enabled 6G.