In the present paper, the leader-following positive consensus problem of fractional-order (FO) multi-agent systems (FOMASs) is investigated. In the system, the dynamics of the agents and the leader are fractional-order linear systems with fractional order \(\alpha \in (0,1]\) , which enables them to utilize historical information. The relationship among the agents is characterized through an undirected graph that is connected and maintains a constant structure. By employing the characteristics of fractional-order stability analysis, characteristics of positive systems and Lyapunov inequality, several necessary and/or sufficient conditions governing the positive consensus of the FOMASs are given. Finally, in order to demonstrate the validity of our theoretical findings, numerical simulations are carried out.