This paper presents a new algorithm for the closed-loop $H_{infty}$ control of a class of singularly perturbed nonlinear systems with an exogenous disturbance, using the successive Galerkin approximation (SGA). The singularly perturbed nonlinear system is decomposed into two subsystems of a slow-time scale and a fast-time scale in the spirit of the general theory of singular perturbation. Two $H_{infty}$ control laws are obtained to each subsystem by using the SGA method. The composite control law that consists of two $H_{infty}$ control laws of each subsystem is designed. One of the purposes of this paper is to design the closed-loop $H_{infty}$ composite control law for the singularly perturbed nonlinear systems via the SGA method. The other is to reduce the computational complexity when the SGA method is applied to the high order systems.