Based on the distributed spherical Gaussian (DSG) polarization potential model, the momentum transfer cross sections (MTCSs) of low-energy electron scattering from H2 molecule are studied with the body frame vibrational close coupling (BFVCC) method and vibrational scattering potentials. The vibrational scattering potentials include the static, exchange, and correlation-polarization contributions calculated based on ab initio method. By including the contributions of 18 Morse vibrational wave functions, 5 partial waves, and 16 molecular symmetries, We obtained well converging MTCSs of ν=0→ν'=0, 1, 2, 3 transition excitations. The comparisons show that DSG polarization potential is a good approximation in the study of low energy electron scattering.