With the explosive development of the Internet of Things (IoT), its security has become a critical concern. As a lightweight hardware primitive, Physical Unclonable Function (PUF) provides a promising solution for IoT security. Nevertheless, as per the knowledge of the authors, most of the existing PUF-based anonymous authentication protocols for IoT are not suitable for end-to-end IoT applications due to their flexibility or security. Specifically, there are two main issues with existing related protocols: (1) the end-to-end anonymous authentication between IoT devices requires the participation of a trusted third party, which seriously affects the flexibility of interaction; (2) most related protocols provide weak anonymity, that is, they are anonymous against only eavesdroppers. To solve these problems, a new PUF-based end-to-end anonymous authentication protocol is proposed. Without needing the real-time participation of the third party, the proposed protocol realizes end-to-end direct mutual authentication and session key agreement while maintaining strong anonymity. It also provides an online dynamic updating mechanism for security parameters. The security analysis shows that the proposed protocol has perfect forward secrecy while resisting various known attacks including physical attacks and modeling attacks. Meanwhile, it outperforms related protocols in terms of protocol rounds and communication costs.