This paper demonstrated a 6.02 kW narrow-linewidth fiber laser based on a one-stage MOPA fiber laser system. At the maximum power, the 3 dB and 10 dB linewidths are 0.36 and 1.47 nm, respectively. The peak signal-to-noise ratio is ~27 dB compared with the Raman Stokes light. The beam quality (M² factor) is ~2.7. To the best of our knowledge, this is the highest power of narrow-linewidth fiber lasers that have ever been reported. In the following work, we will continue to optimize the temporal properties of the seed and the structure of the amplifier to further improve the output power and beam quality of the laser.