Three-dimensional spatio-temporal variation characteristics of pulse intensity is numerically simulated in detail in multi-pass amplifier of high power laser system. Theoretical calculation indicates that the complicated spatio-temporal distortion occurs as the pulse with specific spatio-temporal distribution passes the amplifier. This change imposes some difficulties on shaping prediction of the pulse power. The curve fitting method of input-output integral energy is proposed to achieve the inverse prediction of inject pulse shape formulti-pass amplifier system with high precision. The better prediction result is achieved not only for square pulse shape but also for multiple-steps complex pulse output, the relative power deviation reaches up to 0.032% for the square pulse output, and 0.78% for multiple-steps complex pulse output. In addition, the inverse prediction of more complicated Haan pulse is achieved. The relative power deviation is 0.13%. This method has not only high precision but also rapid computation and strong applicability.