The evolutions of the pulse propagation in gain distributed fiber amplifiers with a finite gain bandwidth are investigated with the simulation of the nonlinear Schrdinger equation. The results show that the parabolic pulse propagations in different gain amplifiers are restricted by the finite gain bandwidth. With the same input pulse and amplifier length and overall gain, the largest energy and best linear chirp output pulse can be obtained from the bidirectional gain distributed fiber amplifier. The smallest and worst linear chirp pulse output can be obtained from decreasing gain distributed fiber amplifier, while pulse obtained from decreasing gain distributed fiber amplifier is between them. Moreover, by choosing smaller initial gain coefficient, the whole gain limited by the gain bandwidth may be larger, linear chirp is better with the same overall gain.