Solving time-dependent Schrdinger equation numerically, we investigate the high-order harmonic generation and ionization probability of one-dimensional, two-dimensional and three-dimensional hydrogen atom exposed to intense laser field. Our results show that high-order harmonic generations and the ionization probabilities of the model atoms and real hydrogen atom are similar both in the multi-photon ionization regime and in the over-barrier ionization regime; in the tunneling ionization regime, the plateau feature and cut-off position of high order harmonic generations of the model atoms and real hydrogen atom are almost the same, and the trend of change of the ionization probabilities with time is similar, but the values of ionization probabilities for the model atoms are different from those for real hydrogen atom. We discuss the reason for the difference of ionization probabilities between the model atoms and the real hydrogen atom according to the classical three-step model.