In order to develop a near-infrared band fiber grating external cavity semiconductor laser for quantum precision measurement applications, a high polarization dependent gain chip and a birefringent fiber Bragg grating were designed independently, the effects of grating reflectivity, external cavity, and chip length on laser linewidth were systematically analyzed based on the Fabry-Pérot equivalent resonant cavity model. The results showe that the developed laser achieves an output power of 54.46 mW, a side mode suppression ratio of 58.88 dB, and a polarization extinction ratio of 24.46 dB. The Lorentz linewidth measured is 2.69 kHz by delayed self-heterodyne beat frequency method. This study provides a reference for the single frequency narrow linewidth external cavity semiconductor lasers with independent design and preparation of discrete devices, and is expected to be used in quantum precision measurement fields such as radar imaging, gyroscopes, magnetometers, and atomic clocks.