Physical model and caculation method are established to describe the laser pulse superpositon in multi-pass amplification process. In this model, the inversion pupulation density is consumed by the pulse leading edge and tailing edge simultaneously. It is demonstrated that this model can not solve the problem of laser superposition amplification in the time-delay coordination. The superposition amplification is solved by building a new time-space coorination. Base on the physical model and caculation method, computer simulation is performed and the pulse shape distortion is discussed at different cavity mirror positions in two-pass amplification process.