The tunable single-frequency (SF) narrow-linewidth fiber laser with all-fiber complex cavity structure is designed, which is composed of an optical fiber tunable filter, a high-precision ring filter, and a fiber loop mirror. A 980-nm semiconductor laser is used as the pumping source, and the ytterbium-doped fiber is employed as the gain medium and saturable absorber, then a wide-spectrum tunable single-frequency narrow-linewidth laser output from 1030 nm to 1090 nm is successfully realized. When the pump power is up to 300 mW, the output power is 18.5 mW and the slope efficiency is 7.95% at the wavelength of 1070 nm. There is no mode hopping phenomenon within 1 h, and the standard deviation of power stability is less than 1%. When the pump power is 200 mW, the linewidth is measured by the delay self-heterodyne method, and the average line width in the wavelength tuning range is 8.7 kHz, and the relaxation oscillation frequency is 64 kHz.