A research has been carried out on the containment control of high-order linear discrete-time multi-agent systems under external disturbances, followed by the design of a discrete-time disturbance observer. By using the observer, an containment control protocol based on state feedback has thus been proposed. With Lyapunov stability theory applied, an analysis has been made of the convergence of the system, thus obtaining the conditions for containment. Finally, the validity of the theoretical results is verified by a numerical simulation.