A compact single-frequency 1060 nm fiber laser based on a high-power semiconductor optical amplifier (SOA) has been proposed and demonstrated with over 40 nm wavelength tuning range. The inhomogeneous gain-broadening feature of the SOA and the unpumped ytterbium-doped fiber-based saturable absorber contribute to the single longitudinal mode lasing of the fiber laser. The maximum 3 dBm output power can be obtained with the optical signal to noise ratio larger than 50 dB. Stable single-frequency operation can be maintained more than 1 h with negligible power fluctuations and low relative intensity noise.