In this Letter, we demonstrate a kilowatt (kW) level high-power fiber laser amplifier with a clear sign of spectral-broadening-free property. The high-power fiber lasing is realized by employing a master oscillator power-amplifier (MOPA) configuration, seeded by a temporally stable random fiber laser (RFL) that utilizes Raman amplification and random distributed feedback from a long passive fiber. The output power reaches 1.03 kW with a 1070 nm wavelength and an optical-to-optical efficiency of 74.6%. Despite the typical nonlinear spectral broadening in most traditional MOPA systems, the output spectral linewidth is well maintained during the whole high-power amplification process. The suppressed linewidth broadening in the spectral domain during high-power amplification is significant for further power scaling, spectral beam combination, and other applications that require narrow-linewidth high-power lasing.