Broadcast multisignature allows multiple signers to sign the same message, which can be used in many areas, such as electronic contract signing, educational administration management system and grade management system. At present, the security of most broadcast multisignature schemes mainly depends on the intractability of large integer factoring (LIF) or discrete logarithm (DL) problem. Thus, broadcast multisignature schemes will suffer from the potential threat of the quantum computing attacks. Hence, it is an important problem how to solve the quantum computing attacks in traditional broadcast multisignature. In this paper, we construct the first certificateless broadcast multisignature scheme based on multivariate public key cryptosystem (MPKC-CLBMSS), whose security is based on the hardness of the isomorphism of polynomials (IP) problem. MPKC-CLBMSS not only solves the problem of quantum computing attacks, but also avoids the key escrow issue in IB-PKC along with the certificate management problem in traditional PKI. In MPKC-CLBMSS, the signature length is as same as that of the partial signature, regardless of the number of signers; the verification time of signature is as same as for a partial signature. MPKC-CLBMSS has higher computational efficiency than the existing broadcast multisignature scheme. Moreover, the security proof shows that MPKC-CLBMSS satisfies the unforgeability in the random oracle model. INDEX TERMSMultivariate public key cryptosystem, certificateless public key technique, broadcast multisignature, post-quantum cryptography.