Abstract: In this paper, the state-feedback stabilizing control design is investigated for a class of high-order nonlinear systems with unknown but identical control coefficients. Although there are system uncertainties, i.e., the unknown control coefficients, no adaptive technique but appropriately choosing design param- eters is available in control design. Here a new approach is put forward to achieve a stabilizing controller for such a class of nonlinear systems. Using the backstepping approach, the design procedure for the stabilizing controller is presented. The designed state-feedback controller preserves the equilibrium at the origin, and guarantees that the closed-loop systems be globally asymptotically stable.