This paper focuses on the positive stabilization problem for a class of switched systems with input time-delay. By introducing the augmented system and taking time-delay as a switching parameter, the positive stabilization problem is converted to the control problem of the augmented system under asynchronous switching. Taking advantage of the properties of dual systems, a sufficient condition is derived to ensure that the augmented system is both positive and stable under the average dwell time switching. Then, a controller is designed to guarantee the prescribed performance of closed-loop systems. Such sufficient condition can be transformed to the normal linear programming problem, which can be solved by using the linprog toolbox in Matlab. Finally, a numerical example is given to illustrate the effectiveness of the obtained results.