Narrow linewidth lasers are the basic components of spectroscopy, precision metrology, and other experiments. Because diode lasers are very sensitive to external optical feedback, the phase noise of diode lasers, can be suppressed by using a high optical feedback bandwidth, enabling the narrowing of the linewidth. In the paper, we use fiber Bragg grating (FBG) as a feedback element and builds a long external cavity feedback loop. In order to reduce the influence of temperature fluctuation of external environment and air flow disturbance, the temperature of the optical fiber is controlled. Then, the maximum temperature fluctuation within 1 hour is reduced from 0.039 °C to 0.003 °C. In addition, the effect of feedback bandwidth on laser linewidth is also tested. Although the bandwidth of the FBG used in the experiment is much larger than the free-running laser linewidth, a narrowing of the laser linewidth is still observed. The smaller the FBG bandwidth, the narrower the laser linewidth. For this phenomenon, we believe that there should be a negative feedback mechanism in the feedback loop, which can stabilize the laser linewidth to a certain slope of the feedback spectrum. Therefore the narrower the feedback bandwidth of the fiber grating, the larger the slope of the feedback spectrum, and the more sensitive the feedback. In addition, by changing the feedback power of FBG in the range of 0~1 mW, it is observed that at the reflected power of 0.8 mW, the optical feedback narrows the laser linewidth from the free-running 100.5 kHz to the narrowest 11.5 kHz, and phase noise in the range of 0.2 kHz to 2 MHz is reduced by about 20 dB.