A 31 kW narrow-linewidth linearly polarized nanosecond all-fiber laser is proposed. The single-frequency continuous laser generated by the seed-source laser is modulated by an electro-optic intensity modulator. To suppress stimulated Brillouin scattering (SBS), the pulse width is set to 2.8 ns, and the repetition rate is 1.59 MHz. After two levels of pre-amplification, and primary power amplification for amplification, the maximum average output power of laser can reach 139 W while the peak power is 31 kW. As stimulated Raman scattering (SRS) is not found during the experiment , the increase in power is limited by SBS. The laser beam quality is less than 1.3 at the maximum output power. The polarization extinction ratio is 14.5 dB, which is limited by the polarization-maintaining (6+1)×1 fiber combiner.