By using the model of multi- photon nonlinear Compton scattering and the transverse dielectric constant formula of electron- positron plasma，the transverse dielectric in the un- magnetized, non- collision, isotropic and ultra- relativistic electron- positron plasma is studied by using the analytic and numerical computing methods. The relativistic Fermi′s distribution under the Compton scattering，the expression of linear dispersion, and the numerical analytic and numerical of the transverse dispersion are given. The results show that the curve length of the short wave in the analytic transverse dispersion is increased in comparison with that before scattering, the curve length of the long wave is decreased, and their positions move to left and upward. The key causesare that frequency of the electron-positron plasma is increased by the scattering, the short wave and long wave components are increased and decreased, respectively. The two discontinuous analytic curves areabsolutely connected by the numerical transverse dispersion curve, so that a smooth curve is formed. The key causes are that the ultra- relativistic probabilities resulting from Compton scattering in the electronpositron plasma are greatly increased, the coupling density and temperature are increased，the high frequency component is decreased，and the whole dispersion composition is increased.