This paper investigates the problem of asynchronously switched stabilising control for a class of switched linear systems with time delay. When there exists asynchronous switching between the controllers and the subsystems, based on the average dwell time (ADT) method, a sufficient condition for exponential stability is developed for a class of switching signals. The condition is delay-dependent and is given in terms of linear matrix inequalities (LMIs). A numerical example illustrates the effectiveness of the proposed method.