A linear consensus protocol for heterogeneous multi-agent systems composed of first-order and second-order agents is proposed. Based on the graph theory and the matrix theory, the sufficient conditions for achieving consensus and consensus equilibrium point are obtained respectively. It is proved that only the initial conditions of the root vertices contribute to the equilibrium point. The convergence interval is deduced. Then, the system can converge to arbitrary expected value in this interval by setting the parameters. Simulation analysis shows the correctness of the proposed theorems.