In this paper, based upon a new concept of the inertial manifolds with delay, a kind of nonlinear elastic rod is studied by an improved version of the nonlinear Galerkin method. This method was employed to project the solutions of the governing equations onto the complete space spanned by the eigenfunctions of equation operators. With the truncation of modes to approach the solution, the original infinite dimensional dynamic system is approximated as a finite one. Furthermore, a timedelay expression which implies the interaction between higher and lower modes was constructed. With the timedelay expression presented, the higher displacement modes were obtained directly without a complicated numerical integration, resulting in a system with less degree-of-freedoms and reducing the computation time.