The containment control for high-order multi-agent systems under fixed directed topologies is investigated in this paper. The control protocols are proposed when the leaders are stationary and dynamical, respectively. For the stationary leaders, using the final-value theorem of the Lapalace transform, the designed linear control protocol drives all followers to converge into the stationary convex hull spanned by the leaders, asymptotically. For the dynamical leaders, the nonlinear protocol is developed to guarantee all followers converge into the dynamical convex hull formed by the leaders. And sufficient conditions of the containment control are proposed. Simulation results validate these theoretical results.