  Quantum molecular dynamic simulations have been employed to study the
equation of state (EOS) of fluid helium under shock compressions. The principal
Hugoniot is determined from EOS, where corrections from atomic ionization are
added onto the calculated data. Our simulation results indicate that principal
Hugoniot shows good agreement with gas gun and laser driven experiments, and
maximum compression ratio of 5.16 is reached at 106 GPa.
