Using the splitting-operator spectral method, the evolution of interaction of the pulse laser with hydrogen atom system was stimulated. The result indicates that when the input laser pulse is sine waves, the Rabi oscillation is also sine waves. When the input laser pulse is amplitude-modulated pulse, the Rabi oscillation will be of square waves, but there exists serious population-leak. Besides, when the hydrogen system is under a confined potential energy, the laser intension can be decreased to decrease the population-leak and achieve complete population transfer.