•The GHz-pulse repetition rate is firstly realized in the wavelength region from 1962 nm to 2005 nm.•The shortest pulse duration is less than 500 fs in the GHz-harmonic mode-locking fiber oscillator.•The average output power reaches to above 340 mW from the GHz-harmonic mode-locking fiber oscillator.•Simulation agrees with the experimental results for the GHz-pulse amplification. The gigahertz (GHz)-pulse repetition rate, 2-μm harmonic mode-locking (HML) Tm-doped fiber oscillator is realized with the nonlinear polarization rotation method. The fundamental pulse repetition rate is 95.8 MHz, which is further increased to 1.25 GHz at 1962 nm, 1.63 GHz at 1982 nm, and 1.05 GHz at 2005 nm with a high super-mode suppression above 37 dB respectively. It is believed to be the first report on the GHz Tm-doped fiber oscillators, which can optionally operate in < 2000-nm or > 2000-nm region. The HML fiber oscillator delivers maximum output powers of 480 mW, 538 mW and 340 mW and at each wavelength, which are the largest output powers never reported from previous GHz 2-μm fiber oscillators. The pulse durations in each wavelength are all < 500 fs. The laser pulse with the highest pulse repetition rate is further scaled up to ∼ 4 W. The observed spectral narrowing and soliton self-frequency shift in the fiber amplifier are further analyzed with a theoretical model, which matches well with the experimental results.