Using the model of multi-photon nonlinear Compton scattering between an electron and a photon-groups, the longitudinal wave dispersion characteristic of the laser-plasma under Compton scattering is studied.The results show that the dispersion curvatures of the long longitudinal wave are formed by the analytic long wave, numerical computing result and short wave. The dispersions of longitudinal wave of the long and short waves are increased with the increase of the characteristic temperatures of the positive and negative relativity electrons, and these dispersions are reduced along with the increase of the frequency increasing number taken place by Compton scattering. The dispersion curvature of the one temperature laser-plasma and the dispersion curvature of the two temperature laser-plasma are similar.