Switched system is an important hybrid system, which is composed of several subsystems and switching signals that determine the switching between subsystems. In engineering applications, there inevitably exists asynchronous switching between the system mode and the controller, i.e., asynchronous switching. The problem of guaranteed cost control of switched time-varying delay systems is investigated under asynchronous switching. A sufficient condition for the existence of the GCC law is derived by using the piecewise Lyapunov function approach and the average dwell time technique, which guarantees the exponential stability and a certain upper bound for the cost function of the closed-loop system. Then, the design problem of the GCC law is solved in terms of linear matrix inequalities, an asynchronous switching GCC controller is designed to make the system robust. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.