Elastic and inelastic differential and integral cross sections for low-energy vibrational excitation of H2 by electron impact are studied with exact exchange. The resulting coupled integrodifferential equations are solved using a combination of linear-algebraic and R-matrix-propagator techniques. The converged (0→0,0→1,0→2) differential and integral cross sections are obtained. The calculated results are in good agreement with experimental resalts and other calculations, showing that the exact exchange based on equations of vibrational close coupling plays an important role in low-energy electron scattering from H2 molecule.