We propose a novel procedure to improve the solution obtained by perturbation methods for analyzing the solutions of strongly nonlinear systems. The multiple-scales method, one of the perturbation method, is widely used in many areas. However, Multiple-scales method fails in analyzing the solutions of oscillators if the oscillator nonlinearity is strong. We apply the proposed procedure to improve the multiple-scales method to obtain the optimum solution of the forced oscillator with strongly nonlinear restoring and inertial forces. The solutions obtained from multiple-scales method and the proposed method are examined by the numerical solution obtained from 4^th-order Runge-Kutta method. The results show that the proposed method is effective for the oscillators with nonlinear restoring force as well as nonlinear inertial force even if the nonlinearities are strong. Numerical results and comparison show that the proposed method can improve the solution lot in comparison to the solution obtained by conventional multiple-scales method.