High-power narrow-linewidth fiber lasers are highly desired for nonlinear frequency conversion, spectral combination, and coherent combination. In this work, a 5 kW near single mode narrow-linewidth fiber laser system is established based on a composite fiber oscillator seed. By optimizing temporal characteristic of seed and structure of amplifier, the stimulated Raman scattering, spectral broadening, and transverse mode instability effects are suppressed comprehensively. Consequently, the output power is scaled up to 5 kW with a slope efficiency as high as approximately 86.1%. The peak signal to noise ratio is about 28.3 dB compared with the Raman Stokes light. The 3 dB and 20 dB linewidths are 0.48 nm and 2.1 nm, respectively. The beam quality (M² factor) is about 1.35. This work shows a amplification potential of narrow-linewidth fiber lasers based on such a simple structure.