Blind signature is a special digital signature, which is widely used in various anonymity environments. At present, the security of most blind signature schemes is mainly based on the intractability of large integer factoring (LIF) or discrete logarithm (DL) problems. However, with the birth of practical quantum computers, the traditional public key cryptosystem will be unsecure; moreover, the quantum algorithms make it face severe challenges. Hence, it is of great value to construct blind signature schemes that can resist the quantum computing attacks. One of main candidates of post-quantum cryptosystems is multivariate public key cryptosystem (MPKC). On the basis of the theory of MPKC and blind signature, a post-quantum blind signature scheme is proposed based on MPKC. The proposed cryptographic scheme separates the public and private keys of the signature by using another nonlinear reversible transformation L:F^r→F^r, which reduces the linear relationship between the public and private keys. Accordingly, it improves the security of the blind signature scheme. Analysis shows that this cryptographic scheme has the blindness, unforgeability, and untraceability; in addition, it has the merits of low computational complexity and resisting quantum computing attacks.