This article concentrate on a fast algorithm for precise integration with dimension expanding method with high accuracy for large scale dynamic structures. In order to improve the accuracy of precise integration with dimension expanding method for large scale dynamic system, the non–homogeneous items are approximated by high order polynomial. To reduce the calculation time, and improve the computational efficiency, a fast algorithm is derived. Numerical example shows that by increasing the approximate order of the non-homogeneous items the significantly improvement of accuracy is obtained, and the fast algorithm can improve the computational efficiency significantly, and the algorithm suit to the long time computation for the large scale dynamic systems.