The amplification of highly chirped pulse with broadband in inhomogeneously broadening amplifier is investigated. Based on the analysis of the properties of the pulse with a very big chirp in which the pulse in time domain and frequency domain shares the same profile and time and frequency are linearly related, a theoretical model for the amplification of highly chirped pulse is built in inhomogeneously broadening medium. The amplification performance of the broadband linearly chirped pulse in the inhomogeneously broadening medium and the feasibility of the shaping compensation of the pulse amplification are explored.