Power propagation equations of multi-pumped fiber Raman amplifier (FRA) were reasonably simplified, and multi-step average power method was applied to compute composite Raman gain of multi-signal in dense wavelength division multi-plexed system (DWDM) amplified by multi-pumped FRA. Based on such a simple and effective model, the influence of the number, input power and wavelength distribution of multi-pump on Raman gain was researched. The rules of implementing the ultra broad and flat Raman gain bandwidth were analyzed. All simulation and analysis provided valuable references for the application of multi-pumped FRA in DWDM system.