In this paper, we study the properties of a set of quantum states. Based on these properties, we propose a multiparty semi-quantum key agreement (MSQKA) protocol. For the sake of clarity, we provide a three-party example to illustrate the protocol. Through rigorous security analysis, it is demonstrated that the proposed protocol can resist both inside attacks and outside attacks, which include Trojan horse attacks, measure-resend attacks, entangle-measure attacks and collective attacks. Besides, the proposed protocol achieves fairness among participants. Finally, we compare our protocol with other SQKA protocols. Compared to previous three-party and MSQKA protocols, our proposed protocol involves more classical parties, needs no external assistance and achieves relatively high key generation efficiency.