A GHz narrow-linewidth high-peak power nanosecond fiber laser based on the master oscillator power amplifier (MOPA) is reported. The modulated distributed feedback single-frequency diode laser seed delivers pulses with wavelength of 1064.12 nm, pulse width of 3.92 ns, and tunable repetition rate from 10 kHz to 50 kHz. A double-pass structure is used in the preamplifier to boost small signal and suppress amplification of spontaneous emission under intense pump. In the power amplifier the stimulated Brillouin scattering is avoided by shortening fiber length. Pulsed laser with 1.5 GHz linewidth and 15 kW peak power is obtained at a repetition rate of 10 kHz. The output pulse characteristics at different repetition rates are studied.