By using a subring cavity incorporated with a saturable absorber, a stable single-frequency selection is realized in a linear-cavity fiber laser, which is constructed using a broadband fiber mirror and a partial reflectance fiber Bragg grating as the cavity ends. At 1550.33 nm, the laser has an optical signal-to-noise-ratio of > 53.28 dB and with linewidth less than 1 MHz. The pumping efficiency is 25% improved by recycling the residual pump power to gain medium. The power stability and wavelength stability have also been studied.