We present a Yb-doped narrow-linewidth polarization-maintaining all-fiber amplifier that achieves a high mode-instability (MI) threshold, high output power, and 9.7-GHz spectral linewidth. Six wavelength-multiplexed laser diodes are used to pump this amplifier. First, we construct a high-power fiber amplifier based on a master oscillator-power amplifier configuration for experiments. Subsequently, we examine the MI threshold by individually pumping the amplifier with wavelengths of 976, 974, 981, 974, and 981 nm respectively. The experimental results demonstrate that the amplifier exhibits a high MI threshold (>3.5 kW) when pumped with a combination of wavelengths at 974 and 981 nm. Afterward, we inject an optimized phase-modulated seed with a nearly flat-top spectrum into this amplifier. Ultimately, laser output of 3.2 kW and 9.7 GHz are obtained.