Effective wavelength extension is vital in the applications of high-power narrow-linewidth fiber lasers. In this work, we demonstrate a 5-kW power-level narrow-linewidth fiber amplifier at 1050 nm utilizing a homemade biconical-tapered Yb-doped fiber (BT-YDF). Up to ∼4.96 kW fiber laser is achieved with a 3 dB linewidth of ∼0.54 nm and a beam quality factor of Mx 2 = 1.46, My 2 = 1.6. The experimental comparisons reveal that BT-YDF has the advantages of improving a stimulated Raman scattering threshold and balancing transverse mode instability suppression in the fiber amplifier. This work could provide a good reference for extending the operating wavelength of high-power fiber amplifiers.