Abstract: Combining the RPTSIM (renewal precise time step integration method) with the basic assumptions of constant average acceleration method of the Newmark family, a new precise integration method is presented and applied to structural seismic response analysis. Calculation formulas and stability of the proposed method are analyzed. When the order of dynamic differential equation is reduced, the size of matrices and equations of the proposed method are only half of that of the RPTSIM. Iterative formulas are straight-forward and the seismic response of displacement, velocity and acceleration can be obtained more conveniently. Although the presented method is conditionally stable, the conditions are very easy to be satisfied. Numerical studies indicate that the proposed method is effective and applicable to analyzing earthquake action.