On the basis of all-normal-dispersion fiber laser, the influences of different pumping schemes on the generation of parabolic pulses are numerically investigated. By establishing the mode of all-normal-dispersion fiber lasers, we have studied the effects of gain saturation energy and gain bandwidth on the fitting factor, pulse width, spectrum width, and pulse energy of the output parabolic pulses. The results show that in backward pumping mode, the laser can output parabolic pulses with higher energy, and can generate parabolic pulses with lower gain saturation energy. The backward pumped all-normal-dispersion fiber laser can maintain the output of the parabolic pulses in a larger gain and saturation energy range. The gain bandwidth of gain fiber has a small influence on the output characteristics of the parabolic pulses in different pumping schemes.