In this study, the electron energy distribution function (EEDF), the electron swarm parameters , the effective ionization coefficients, and the critical field strength (dielectric strength) in binary He-H2 gas mixture which is used as cryogenic for high-temperature superconducting power applications,  are evaluated using two-term solution  of the Boltzmann equation over the range of E/N ( the electric field to gas density) from 1 to 100 Td ( 1 Td=10-17 Vcm2) at temperature 77 K and pressure 2MPa, taking into account elastic ( momentum transfer) and inelastic cross-sections. Using the electron energy distribution function (EEDF) electron swarm parameters (electron drift velocity, mean electron energy, diffusion coefficient, electron mobility, ionization and attachment coefficient) are calculated. At low reduced electric field strength E/N, the EEDF is close to Maxwellian distribution, at high E/N, due to vibrational excitation of H2, the calculated distribution function is non-Maxwellian. Besides, the Boltzmann equation analysis showed as the small mole fraction of H2 in the He-H2 mixture is increased, the electron energy distribution function EEDF shifts to lower energy region, the density-reduced ionization coefficient α/N and density-reduced effective ionization coefficient (α-η)/N decreases, whereas density-reduced attachment coefficient η/N, density-reduced critical electric field strength increases, (E/N)crt  and critical electric field Ecrt  increases. It is found that dielectric field strength depends on pressure and temperature. To confirm the validity of the two term solution of Boltzmann equation analysis, a set of elastic and inelastic cross-sections for each gas He and H2 are used to calculate the electron swarm parameters and dielectric field strength. Compared with previous experimental and theoretical literatures, the values obtained are generally in good agreement.