As quantum computing technology matures, it poses a threat to the security of mainstream asymmetric cryptographic methods. In response, the National Institute of Standards and Technology released the final version of post-quantum cryptographic (PQC) algorithm standards in August 2024. These post-quantum cryptographic algorithms are primarily based on lattice-based and hash-based cryptography. Therefore, this study proposes the Post-Quantum Cryptography Winternitz-Chen (PQCWC) anonymous scheme, aimed at exploring the design of anonymous schemes based on PQC for future applications in privacy protection. The anonymous scheme designed in this study is mainly built on the Winternitz signature scheme, which can prevent the original public key from being exposed in the certificate. Furthermore, the PQCWC anonymous scheme integrates the butterfly key expansion mechanism, proposing the first hash-based butterfly key expansion mechanism in the world, achieving anonymity for both the registration authority and the certificate authority, thereby fully protecting privacy. In the experimental environment, this study compares various hash algorithms, including Secure Hash Algorithm-1 (SHA-1), the SHA-2 series, the SHA-3 series, and the BLAKE series. The results demonstrate that the proposed anonymous scheme can achieve anonymity without increasing key length, signature length, key generation time, signature generation time, or signature verification time.