Abstract: In this paper, a rapid simulating method for the linear continuous system inputted with the first class typical function is proposed and discussed. High accurity and value-stability are advanteges of this method. And it can be used to simulate the system in which other methods used are not convergent in some sample period length. In addition, an analytic algorithm is presented to acquire the anwser for the inear system and the systems containing compound characteristic roots. The state prolificative method for the "auonomy" of linear system and the initial value transferring method for the system described by high-order differential equations are also provided in the paper.