This paper is concerned with the problem of robust H-infinity control for a class of nonlinear systems with parameter uncertainty. The system under consideration is composed of two cascaded subsystems : a zero-input asymptotically stable nonlinear one and a linearizable one which is controllable. The uncertain parameters are from a known compact set and are allowed to enter the system nonlinearly. Based on a Lyapunov approach, a nonlinear static-state feedback controller is designed such that the L-2-gain of the closed-loop system is below a prespecified value for all admissible uncertainties. Furthermore, the closed-loop system is shown to be robust input-to-state stable under some conditions.