Secure multi-party computation (MPC) protocols do not completely prevent malicious parties from cheating. Though numerous researches on cheating detection are proposed, most cheater detection works do not guarantee fairness of the protocol. That is, if the corrupted parties try to violate fairness, the output of the computation can only be obtained by themselves, but not by the honest parties. In this paper, based on the SPDZ framework, we propose a fair secure multi-party computation protocol with honest-majority by using identifiable secret sharing. This protocol can identify corrupted parties during the execution process and prevent them from undermining the fairness of the protocol. In addition, the protocol satisfies publicly auditability, which allows any third party to verify the correctness of the protocol’s output results. The security of the protocol was proved in the universal composability framework. The protocol maintains high online efficiency when no cheating happens. And if corrupted parties try to violate the fairness, honest parties need to expend additional computation to regain the output results of the protocol, but the cost remains within a reasonable range.