Abstract: Method of trigonometric series is one of methods widely used for syhthesizing artificial ground motion. However, the compution errors,which are similar to the classic baseline shift, are found in integrated acceleration time history. An analytic formula for calculating integrated velocity time history is deviated in detail, and compution errors are analyzed emphatically. The study proves that the strength envelope function will produce compution errors of integrated velocity time history, if there are non differentiable singular points in it. On this basis, a new modified method is put forward.