<p>This paper investigates the stabilization problem of switched neutral systems under asynchronous switching. In contrast to the existing results, a less conservative dwell-time-based condition that the dwell time of sub-modes is larger than the difference between the upper bound and the lower bound of switching delay is employed. By using multiple Lyapunov functionals, some sufficient conditions in the form of linear matrix inequalities to solve the stabilization problem are proposed under the mode-dependent average dwell time constraint. A simple numerical example is utilized to reveal the validity and superiority of our work.</p>