A single-frequency master-oscillator fiber power-amplifier operating at 1991 nm was demonstrated. The seeding laser was a diode-pumped, high efficient, single-longitudinal-mode Tm:YAP laser with a coupled-cavity configuration. 721 mW single-frequency output power was obtained at 1991 nm, the slope efficiency was 46%. The power amplifier was a diode-pumped Tm-doped fiber. 8.6 W single frequency output power was obtained from the amplifier. The maximum output power was limited by the low coupling efficiency of the seeding signal into the fiber core. The strength of ASE in the fiber amplifier with respect to the power of input signal was studied experimentally. High power single-frequency lasers at 2 μm optical region have potential applications on eye-safe coherent lidar and optical remote sensing.