A new method for model order reduction for an important class of nonlinear dynamical systems is proposed. The reduction technique is based on the frequency balance reduction method within a desired frequency band and a developed trajectory piecewise-linear (TPWL) model order reduction approach. Both of the methods are recently developed techniques and they can increase the accuracy and efficiency of the reduction method. The computational load and memory is significantly reduced when the method is used in the hybrid reduction method. The accuracy enhanced hybrid method is applicable to very large scale nonlinear models efficiently and accurately. The numerical results show the accuracy and efficiency enhancement of the proposed method.