Abstract: A precise time step integration method (PTSIM) applied for linear time-invariant dynamic system with non-homogeneous vectors is presented, which is of the same accuracy of the precise time step integration method of general solution. Firstly, the domain of integration is separated into sections. And then a particular solution in the form of integration is chosen and is solved by precise numerical algorithm. Secondly, when the non-homogeneous vector is kind of polynomial, exponential function or trigonometric function, the integration can be converted to a recursion. So the particular solution in the form of integration is precisely obtained by only matrix multiplications. The merit of the new PTSIM is that the process of calculating the general solution and the one of calculating the particular solution are organically combined together. And it is of high precision, efficiency and widely applicability. Numerical examples are given to demonstrate the validity and efficiency of the new PTSIM.