By focusing on a typical emitting wavelength of 1120 nm as an example, we present the first demonstration of a high-efficiency, narrow-linewidth kilowatt-level all-fiber amplifier based on hybrid ytterbium-Raman (Yb-Raman) gains. Notably, two temporally stable, phase-modulated single-frequency lasers operating at 1064 nm and 1120nm, respectively, were applied in the fiber amplifier, to alleviate the spectral broadening of the 1120 signal laser and suppress the stimulated Brillouin scattering (SBS) effect simultaneously. Over 1 kW narrow-linewidth 1120 nm signal laser was obtained with a slope efficiency of ~ 77% and a beam quality of M2~1.21. The amplified spontaneous emission (ASE) noise in the fiber amplifier was effectively suppressed by incorporating an ASE-filtering system between the seed laser and the main amplifier. Further examination of the influence of power ratios between the two seed lasers on the conversion efficiency had proved that the presented amplifier could work efficiently when the power ratio of 1120 nm seed laser ranged from 31% to 61%. Overall, this setup could provide a well reference for obtaining high power narrow-linewidth fiber lasers operating within 1100-1200 nm.