The momentum transfer cross sections （MTCSs） of low-energy electron scattering from H2 molecule are studied using the body frame vibrational close coupling method and the electrostatic potential, the exchange potential,and the correlated polarization potential calculated based on ab initio method. By considering the contributions of 18 Morse vibrational wave functions, 8 partial waves, and 16 molecular symmetries, we obtain the converged MTCSs of ν=0→ν′=0,1,2,3,4 transition excitations. The converged total MTCSs agree well with the recommended values of Elford et al., and are better than the previous theoretical studies in the eletron energy range of 1 eV