A theoretical investigation on the differential cross section (DCS) from low-energy electron scattering of high-lying vibrational excited 112 molecules is reported. The body-frame vibrational close-coupling (BFVCC) approach is used to solve the scattering equations. Quantum scattering potentials include static, exchange, and polarization contributions based on ab initio calculations. By including the contributions of 9 partial waves (Ne=9), 18 Morse vibrational states (Nv = 18), and 16 molecular symmetries (A=0, 1,..., 7), the calculated DCSs have good agreement with available experimental measurements and theoretical studies, and show that high angular momenta and good vibrational wavefunctions are necessary to better describe the scattering physics of electron-molecule vibrational excitation collisions.