A sub-kHz linewidth single-frequency fiber laser that can be tuned in the full range of C + L band is proposed and experimentally demonstrated. A broad band gain fiber by bidirectional pumping combining with a wide tunable filter is used to realize 75.87 nm tuning range from 1529.98 to 1605.85 nm, which can be further improved if a wider tunable filter is available. To achieve single-frequency ultra-narrow linewidth laser operation, a ring-cavity laser configuration with a fiber sub-ring and a saturable absorber is utilized. The measured optical signal-to-noise ratio (OSNR) of the fiber laser is over 80 dB, the side mode suppression ratio (SMSR) can be improved to ∼60 dB, and the linewidth can be narrowed to ∼453 Hz. The output power of the laser exceeds 28 mW, and the slope efficiency is 2.05 %. This proposed fiber laser has the advantages of narrow linewidth, excellent wavelength tunability, and high output power, which is promising for the applications in optical sensing and optical communication systems.