Single-stage high-power narrow-linewidth fiber laser has been investigated intensively recently because of its simple and robust configuration and great potential in spectral/coherent beam combination. In this work, a 6 kW narrow-linewidth fiber amplifier was experimentally achieved based on a fiber oscillator seed. By employing a few-mode ytterbium-doped fiber, the spectral broadening and SRS effects are both significantly mitigated. Combined with a wavelength-stabilized 981 nm pump source, the threshold of transverse mode instability is improved, then, a maximum output power of 6020 W at the central wavelength 1080 nm was achieved with 3-dB bandwidth of ~0.37 nm and optical-to-optical efficiency of ~85.6%. The mode instability and nonlinear effects were balanced well. The measured beam quality and the signal to Raman ratio were M 2 ~2.7 and ~27 dB, respectively. This work shows the great potential of such amplification structure for the power scaling of high-power narrow-linewidth fiber lasers.