In this article, we consider the sampled-data leader-following consensus problem for a class of general linear multiagent systems over both static directed networks and switching directed networks. A distributed asynchronous sampled-data state feedback control law is proposed. We show by Lyapunov analysis that the problem can be solved by the proposed control law as long as the sampling periods of all agents are smaller than a given threshold, which can be explicitly calculated. An example is given to illustrate the effectiveness of our approach.