A low noise single-frequency 1 083 nm fiber laser with a linear cavity was presented and demonstrated with a linewidth of 4 kHz. A polarization controller was introduced to eliminate the spatial hole burning effect in the linear cavity to suppress the multiple longitudinal mode oscillation. The results show that, when the pump power is in the range of 40 mW～200 mW, the single-frequency oscillation is very stable, the maximum output power can reach to 46 mW, the optical signal to noise ratio is larger than 60 dB, the maximum optical-to-optical conversion efficiency and the slope efficiency is 23% and 33.3%, respectively. The stable single-frequency operation can be maintained more than 1 hour with the instability of the output power and the spectrum fluctuations less than ±3% and 0.9% respectively. There are no mode hopping and mode competition during the entire observation.