Most of the existing blind proxy re-signature schemes are designed based on the traditional public key cryptosystems, whose security relies on the hardness of big integer factoring, discrete logarithm, elliptic curve discrete logarithm, and so on. However, these problems will be unsecure when facing the attack of quantum computers. Motivated by these concerns, we proposed a blind proxy re-signature scheme based on the problem of isomorphisms of polynomials, which can resist quantum attack, and gave its security proof under the random oracle model. In the proposed scheme, the message can be kept blind by using the hash function, and the delegatee's identity can be kept anonymous by using the problem of isomorphisms of polynomials. Compared with the existing schemes, the new scheme has more secure properties, such as quantum resistance, high efficiency, message blindness, and delegatee anonymity. It is concluded that the proposed scheme has a good application prospect in the future quantum computing environment with low-power hardware.