The high order harmonic generation (HHG) of hydrogen molecule irradiated by ultra-strong femto-second laser pulse is simulated by the TTDFT method with the classical and quantum combination technique. The results indicate that the HHG spectra of H2 have a “decrease-plateau-cutoff” structure. A kind of “odd allowed, even forbidden” selective phenomenon of the order number of HHG is observed. Change in polarization direction of laser beam may change the cut-off order and spectrum intensity of HHG simultaneously.