This paper is concerned with the robust stabilization of multiple time-varying delays system with norm bounded nonlinear perturbations. By constructing an appropriate Lyapunov functional, dealing with the cross terms in the functional derivative by using the Jensen inequality, and utilizing the linear matrix inequality technique and Schur complement lemma, we obtain the system stabilization delay-dependent sufficient condition and a memory state feedback controller design method. Finally, a numerical example is proposed, which shows the stabilization condition is less conservative and the effectiveness of the memory state feedback controller.