Taking the group velocity dispersion, Kerr nonlinear effects, gain saturation and gain spectrum of gain medium into account, a equation describing the propagation of optical pulse in the medium is derived. The propagation state of a high power linear chirped pulse in the gain medium is simulated numerically using Split-step Fourier transform method, and the influence of gain dispersion on the profile and power spectrum of optical pulse is discussed emphatically. The results show that when propagating and amplified in the gain medium, the high power super-Gaussian optical pulse′s shape becomes sharp, peak moves to pulse front edge, the spectral peak moves to lower frequency, and the asymmetric oscillation structure is formed in spectral edge. When the gain dispersion of medium increases, the spectrum width of optical pulse becomes narrow, and its peak power decreases. As a result, the gain dispersion will cause loss of the broadband spectrum pulse.