Abstract: Multi-party concurrent signatures were first proposed by Tonien et al at ISC2006, but Xie and Tan pointed Tonien et al’s scheme doesn’t satisfy fairness and they reconstructed multi-party concurrent signature schemes respectively. Through analysis, the multi-party concurrent signature schemes proposed by Xie and Tan don’t satisfy fairness either, so a formal security model of fair multi-party concurrent signatures was proposed and a multi-party concurrent signature scheme based on bilinear pairing and multi-party key agreement was also reconstructed. Analysis shows that the new scheme satisfies correctness, unforgeability, ambiguity, concurrency and fairness in the random oracle model assuming the CDH problem is intractable and highly efficient in signature size, computation cost and communication cost compared with other schemes of its kind.