Optical limiting (OL) and dynamical two-photon absorption (TPA) of 4,4'-bis(di-n-butylamino)stilbene (BDBAS) molecules in chirped femtosecond laser pulses are studied by solving Maxwell-Bloch equations with an iterative predictor-corrector finitedifference time-domain (FDTD) method.It shows that both sign and magnitude of chirp rate influence greatly spectrum evolution and OL behavior.Spectra exhibit obvious carrier frequency shifts depending on sign of chirp rate,blue shift for positive chirp rate and red shift for negative chirp rate.As absolute chirp rate increases,shift becomes more obvious,OL window gets narrower and saturation of output intensity becomes greater.Interestingly,self-induced transparency (SIT) appears as a negative chirp rate reduces to a certain value (-0.025 fs^-2).Dynamical TPA cross section is reduced as chirp effect is considered.It provides a method for controlling nonlinear optical absorptions.