Based on semiclassical approach, the transport equations of chirped-pulse amplification are presented. Time-and spectral-domain evolution of chirped pulse and effects of self-phase modulation in multipass amplification are numerically analyzed. Theoretical results show that the new frequency chirp induced by self-phase modulation changes the instantaneous frequency of chirped pulse and affects the quality of amplified pulse. The study of chirped-pulse amplification in the gain saturation regime shows that the linear frequency chirp of input pulse tends to suppress the effects of self-phase modulation.