A dual-order Raman fiber laser (RFL) with stabilized output power is proposed and theoretically analyzed. The results show that the first- and second-order Stokes output powers are hardly impacted by the pump power fluctuations due to the clamping mechanism induced by the amplified spontaneous emission near the second-order Stokes shift from the launched pump line. As a result, the low-frequency relative-intensity-noise transfer from the pump power to the laser outputs is greatly suppressed. The results show that the first- and second-order Stokes are both stable. In addition, their powers can be tuned by adjusting one attenuator in the RFL setup. These special behaviors predict that the proposed RFL is highly suitable to be the pump sources in Raman fiber amplifiers.