Optical signal-to-noise ratio (OSNR) is one of the most significant parameters for the performance characterization of random fiber lasers (RFLs) and their application potentiality in sensing and telecommunication. An effective way to improve the OSNR of RFLs is pump scheme optimization, for example, employing a temporally stable source as the pump. In this paper, the output performance of an incoherently pumped RFL dependence on the pump bandwidth has been investigated both in experiment and theory. It is found that a high-OSNR RFL can be achieved with broadband amplified spontaneous emission (ASE) source pumping, and a relatively broad pump bandwidth can also help suppress the spectral broadening while maintaining an ultra-high spectral purity. By optimizing the pump bandwidth to ～10nm, maximum OSNR of ～39dB (corresponding to a spectral purity of ～99.96%) with more than 99 W output power can be obtained. Moreover, for the pump bandwidth of 0.6–40 nm, the spectral purity can reach as high as >99% with the pump power ranging from ～85 to ～117W. In addition, with the aid of theoretical simulation based on a modified power balance model, we find that the increment of pump bandwidth can decrease the effective Raman gain coefficient, further influencing the gain characteristics, nonlinear effects, and eventually the output performance. This work provides new insight into the influence of the pump characteristics on the output performance of incoherently pumped RFLs.