The generation of group delay ripple and reflection sideband is explained by the oscillazation theory. And the effect of non-constant change of averaged index modulation induced by the one-side exposure apodization on the characteristics of chirped gratings is analyzed for the first time. The mechanism of apodization to enhance the performance of chirped fiber Bragg gratings is studied also. Based on the study, a simple apodization method to improve the performance of chirped fiber gratings is proposed, in which only one-sided exposure is needed which is easy to realize.