We demonstrate a high-power narrowband all-fiber superfluorescent fiber source employing three-stages master oscillator power-amplifier chain. Narrowband seed light is selected from a broadband-amplified spontaneous-emission source by a spectrum filter combing with fiber circulator and fiber Bragg grating. In the main amplifier, the maximal output power is 1.87 kW with an optical-to-optical conversion efficiency of 77.4% and a full width at half-maximum (FWHM) linewidth of 1.7 nm. The corresponding power fluctuation is ±1.4% in 100 s operation, and no parasitic oscillation or self pulsation is observed. A beam quality of M(2)=1.71 is measured at 1.4 kW output power. This manuscript investigates the spectral evolution in high-power amplification. The central wavelength shifted from 1079.5 nm to 1080.7 nm, and the FWHM linewidth narrowed from 2 nm to 1.7 nm at full power, respectively. These effects could be inferred as hybrid effects of many factors, such as wavelength shifting of pump LD, nonoptimized length of gain fiber, and enhancement of temperature level of gain fiber. The narrowband-maintained characteristic in spectral domain under high-power amplification is significant for applications such as spectral beam combination, and further power scaling is available as the output power is only limited by the pump power.