We demonstrate a single longitudinal mode distributed Bragg reflection (DBR) fiber laser by directly fabricating fiber Bragg gratings (FBGs) on an ytterbium-doped fiber (YDF) using a femtosecond laser. A simple optical self-injection feedback method was used to effectively compress the linewidth and reduce relative intensity noise (RIN) of a single longitudinal mode DBR fiber laser. Further, we investigated the effect of self-injection feedback cavity length and reflectivity on linewidth compression and determined that the linewidth tends to decrease with the increase of the external cavity photon lifetime. By a self-injection feedback, the laser linewidth was compressed from 31.8 kHz to 1.4 kHz. Meanwhile, the relaxation oscillation peak from -103.2d B/H z at 1.51 MHz was suppressed to -122.3d B/H z at 0.16 MHz. This low-noise narrow linewidth single longitudinal mode fiber laser is expected to be a promising candidate for applications such as active detection of neutral atmosphere and distributed fiber sensing.