ing at the three-dimensional inversion problem of high power laser multi-pass amplification, we propose two inversion methods. The first method is a modified gain iterative algorithm based on the curve fitting method of input-output integral energy. The second method is a forward iterative algorithm based on the modified input pulse. In the four-pass amplification with gain distribution, the two methods are verified by numerical simulation. The results show that the two iterative algorithms are effective and feasible, and the three-dimensional intensity distribution of spatio-temporal separation of input pulse can be obtained. The calculated output pulse is basically the same as the demanded value. The relative deviation of the output energy is less than 10 ^-7. The relative deviation of the power waveform obtained by the first method is less than 1%, and this value is less than 10 ^-6 for the second method. The spatio-temporal evolution distortion caused by the saturation effect is solved. The first method relies mainly on the consistency of the forward and inverse model, which is relatively straightforward. The second iterative algorithm introduces a feedback factor, and has high precision and strong expansibility.