Based on the ideas of the nonlinear Galerkin method and post-processed Galerkin method, the predictor-corrector Galerkin method is proposed to deal with the order reduction of large-scale nonlinear dynamical systems. In the modal coordinate, a large-scale nonlinear dynamical system is split into a ‘dominant’ subsystem, a ‘slave’ subsystem, and a ‘negligible’ subsystem. Neglecting the effects of the ‘negligible’ subsystem, a novel predictor-corrector algorithm is developed to deal with the ‘dominant’ subsystem and the ‘slave’ subsystem. In such a way, a lower reduced order system can be obtained to maintain the accuracy and save the computing time. A low-pressure rotor-bearing model of 200MW turbine set is given to illustrate the accuracy and efficiency of the predictor-corrector Galerkin method in comparison with the standard Galerkin method. It shows that the novel method gives a considerable increase in accuracy for little computational cost.