We demonstrate an all-fiber high-power narrow-linewidth fiber laser based on a homemade tapered Yb-doped fiber (T-YDF). The laser performance is investigated and systematically compared with different seed powers and pump manners. The experimental results reveal that the injected seed power requires a trade-off designed to take into account the impact of spectral broadening, nonlinear effects, and transverse mode instability (TMI). Compared with the co-pump manner, the counter-pump manner performs well in inhibiting nonlinearities, spectral broadening, and improving the TMI threshold. Under the counter-pump manner, this narrow-linewidth T-YDF amplifier realized a 2.09 kW output power with a 3 dB spectral linewidth of ∼0.34 nm, a beam quality of M2∼1.28 and a high Raman suppression ratio over 53.5 dB, the highest reported power for such a T-YDF-based narrow-linewidth single-mode laser, to the best of our knowledge. This work provides a promising pathway towards implementing monolithic high-power narrow-linewidth single-mode fiber lasers.