Based on a lumped model of a passively mode-locked Yb-doped fiber laser, the influence of the limited gain bandwidth on the laser′s output characteristics is investigated numerically. Simulation results show that the duration of the output pulse and the operating regimes are determined by the gain bandwidth. The pulse duration increases with the gain bandwidth increasing. By changing the intra-cavity average dispersion monotonically, it is demonstrated that under the condition of wide gain bandwidth, the laser operates in the self-similar regimes under a large range of cavity parameters. In addition, the interaction of pulse pair in distinct gain bandwidth is also studied. Simulation results show that the nonlinear phase shift plays an important role in pulses interaction, and the nonlinear phase shift is determined by the gain bandwidth, therefore the wider gain bandwidth leads to the stronger interaction forces between the pulses.