Based on the characteristics of linearly chirped pulse, a numerical model for amplification of broadband chirped pulse in the inhomogeneous broadening system has been established. The basic idea of this model is that the input chirped pulses are considered to consist of many quasi monochromatic pulses having different center frequencies and intensities, thus using the Frantz-Nodvik model the amplification is calculated. Numerical simulations indicate that the inhomogeneous broadening system astmell as the homogeneous one has the effects of gain narrowing and pulse distortion, however, in the output pulse of the inhomogeneous broadening system, the leading edge will undergo the same amplification as the trailing edge, and the spectrum is symmetrical to the center frequency. In addition, while the spectral bandwidth of the input pulse increasing, both gain narrowing and pulse distortion are becoming more serious, and the profile of output pulse is growing more similar in shape to the lineshape of the inhomogeneous broadening system.