This brief paper addresses the finite-time stability problem of switched positive linear systems. First, the concept of finite-time stability is extended to positive linear systems and switched positive linear systems. Then, by using the state transition matrix of the system and copositive Lyapunov function, we present a necessary and sufficient condition and a sufficient condition for finite-time stability of positive linear systems. Furthermore, two sufficient conditions for finite-time stability of switched positive linear systems are given by using the common copositive Lyapunov function and multiple copositive Lyapunov functions, a class of switching signals with average dwell time is designed to stabilize the system, and a computational method for vector functions used to construct the Lyapunov function of systems is proposed. Finally, a concrete application is provided to demonstrate the effectiveness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.