Abstract: The energy conversion efficiency of the multi-photon nonlinear Compton scattering in the cone-shaped femto-second high power laser-plasma is given by using the inelastic collision model of relativistic electron and photon,and relativistic electricity theory.We find that the vibration of the electron acceleration energy is takenplace by the coupling laser field in the laser-plasma,and the energy conversion efficiency is lowered by the electrostatic field.The greatest energy conversion efficiency of the elect...