Abstract: The present nonlinear dynamic system governed by the equation , is transformed to that governed by the equation , in which , and are respectively linear homogeneous part, nonlinear part and non-homogeneous load item in the right terms of the equation. Combining the precise integration method and Adams-Bashforth-Moulton’s predict-correct multi-step method, a highly precise multi-step method for nonlinear dynamic equations is established. Compared with the present Adams-Bashforth-Moulton method through the numerical results, the high accurate and stable advantage of the presented method has been shown, suitable to calculate the seismic response of structural systems with multi-degrees of freedom.