Based on the coupled mode theory, by using the time-domain transfer matrix method, the bistable characteristics of nonlinear Bragg gratings (NLBG) are analyzed numerically. The results show that under steady case, various tapered factors have a different effects on the threshold switching energy and also positive and negative taper can cause the response of optical isolator in NLBG. On the other hand, with the continuous wave taken into consideration, the periodic self-pulsation may emerge extremely easy under the dynamic conditions in NLBG. As the input power increases to the critical intensity, the self-pulsation transforms into the chaos. For a certain tapered factor, the pulsation width and the frequency of the self-pulsation will reduce with the increase of coupling coefficient, but the output state will transform into relaxation damped oscillation when the coupling coefficient reaches a certain value.