By using the state-dependent switching control strategy, the switching rule design for global exponential stability with H_∞ performance of uncertain switched nonlinear systems with time-varying delay is considered. By using a Lyapunov-Krasovskii(LK) function technique, sufficient conditions for the existence of a class of stabilizing switching laws are derived in terms of linear matrix inequalities(LMIs) to guarantee the switched time delay system to be exponentially stable. The free weighting matrix and integral-inequality approaches are used to find the less conservative stability results. Numerical examples are provided to show the effectiveness and less conservativeness of the proposed methods.