Aiming at the lag consensus problem of first-order and second-order hybrid heterogeneous multi-agent systems, a distributed lag consensus control protocol based on pinning control was proposed. Firstly, the lag consensus analysis was transformed into stability verification. Then, the stability of closed loop system was analyzed by using graph theory and Lyapunov stability theory. Finally, the sufficient conditions for solvability of lag consensus based on Linear Matrix Inequality (LMI) were given under fixed and switching topologies respectively, so that leader-follower lag consensus of heterogeneous multi-agent system was achieved. The numerical simulation results show that, the proposed lag consensus control method can make the heterogeneous mult-agent systems achieve leader-follower lag consensus.