This study investigates an asynchronous switching state feedback control problem for discrete impulsive switched delay systems with average dwell time. A novel time-varying multi-Lyapunov–Krasovskii functional approach is adopted to establish the control synthesis conditions that guarantee the exponential stability of the closed-loop systems. The relation between the upper bound of asynchronous switching delay and the stability conditions is also explicitly given, and the overall conservativeness of the stability results is improved over the existing results. A numerical example is provided to illustrate the effectiveness of our theoretical results, where the comparison with the existing results demonstrates significant improvement using the proposed method.