Abstract: It is proposed that a chirped pulse can be better amplified using a chirped electron beam at an free-electron laser (FEL), and the reasons of which and the effects of the slippage between the optical and electron beams are analyzed. The processes of the FEL amplifier with energy-chirped beam amplifying chirped pulses with different chirped parameters are studied through numerical simulations using our 1D time-dependent code GOFEL-P. The peak power and width of the final compressed pulse with different chirped parameters have been computed. The results show that, comparing with a normal electron beam, the energy-chirped beam can amplify chirped pulse with larger chirped parameter, and the peak power of the final compressed pulse can even reach near 10 times larger and the width of the pulse