A low-threshold Raman effect in a kilowatt ytterbium-doped narrowband fiber amplifier system is reported. The Raman Stokes light at 1120 nm is achieved with the total output power of only ～400 W, indicating that the Raman threshold of this kilowatt codirectional pumped continuous wave fiber amplifier is much lower than the predicted value estimated by the classic formula. To figure out the mechanism of this phenomenon, simulations based on the general stimulated Raman scattering (SRS) model are analyzed indicating that the key factor is the coupling between four-wave mixing (FWM) and SRS. The simulation results are in good agreement with our experiments.