Abstract: The precise time-integration method proposed for linear time-invariant dynamic systems can give precise numerical results approaching the exact solution at the integration points. However, difficulty arises when the algorithm is applied to the non-homogeneous dynamic systems due to the inverse matrix calculation and the simulation of the applied loading. By combining the Gauss quadrature with the calculation technique of matrix exponential function in the precise time-integration method, a new precise time-integration method, Gauss precise time-integration method, is proposed. The new method avoids the inverse matrix calculation and the simulation of the applied loading and improves the computing efficiency. The order of accuracy is selectable in the method. A numerical example is given to demonstrate the validity and efficiency of the method.