An ultra-narrow linewidth full C-band tunable single-frequency linear-polarization fiber laser based on self-injection locking has been demonstrated. By the use of a tunable narrow-band fiber Fabry-Perot interferometer, the laser wavelength could be flexibly tuned from 1527 to 1563 nm with linewidths of < 700 Hz. The laser frequency noise is less than 40 dB re Hz/Hz1/2 at low frequencies (< 100 Hz) and reaches -5 dB re Hz/Hz1/2 at around 25 kHz. The measured relative intensity noise (RIN) is less than -130 dB/Hz with regard to frequencies of over 3 MHz, while the obtained linear polarization extinction ratio (LPER) is higher than 28 dB. This ultra-narrow linewidth low-noise tunable single-frequency linear-polarization fiber laser provides a promising candidate for high-order quadrature amplitude modulation (QAM) optical communication system.