Abstract: Robust H_∞ control problem of nonlinear systems with time-varying delay and polytopic uncertainty is discussed. The nonlinear condition satisfying a type of especial linear bound is assumed. By using the linear matrix inequality technique, a sufficient condition for nonlinear time-delay systems, which is asymptotically stable and satisfies H_∞ performance, is given, and the explicit design method of the robust H_∞ controller is obtained. Finally, an numerical example is supplied to clarify the feasibility and effectiveness of the proposed results