Abstract: An integral-equality approach for studying time-delay systems was extended to investigate switched systems with time-varying delays. A new approach which can analyze switched systems with time delays was proposed, and this approach gives sufficient conditions and switching design of linear switched systems with time delays. According to the rules in the choice of free terms, the free weighting matrices were investigated to construct a integral equality. Less conservative stability criteria can be obtained because no extra conservative is introduced. An example was given to show the validity of the presented method.