We have developed a high power tunable single-frequency 1064 nm quasi-continuous-wave laser oscillator-amplifier system. By controlling precisely the temperature of etalon in the three-mirror ring traveling-wave oscillating cavity viz. adjusting refractive index and thickness of material to tune laser wavelength, 13.2 W 1064 nm single-frequency quasi-continuous-wave oscillating light with tunable range of 58 GHz is obtained, at repetition rate of 1 kHz and duty ratio of 10%. After the laser beam from the oscillator transfers through the amplifier with two laser heads, the output of the oscillator is amplified to be 44 W and the beam quality factor M2 is measured to be 1.58.