Single-longitudinal-mode（SLM） fiber lasers are recognized for their narrow linewidth， high coherence， excellent beam quality， and ease of integration， making them indispensable for a wide array of applications， including coherent optical communication， LiDAR， and gravitational-wave detection. Their ability to generate high-quality， stable， narrow-linewidth light is crucial for ensuring the integrity and precision required in these fields. Additionally， distributed Bragg reflector（DBR） SLM fiber lasers provide several key advantages， such as flexible wavelength tuning， mode-hop-free operation， and relatively low fabrication costs. These benefits have contributed to their growing adoption across various industries and research areas. However， the output performance of DBR SLM fiber lasers is heavily influenced by the intracavity fiber Bragg grating（FBG）， whose spectral characteristics directly impact critical parameters such as linewidth， side-mode suppression ratio（SMSR）， wavelength stability， and output power. Consequently， precise control and accurate characterization of FBG parameters are essential for optimizing the performance of DBR SLM fiber lasers.This study investigates the design， characterization， and application of FBG in DBR resonators for SLM laser generation， following a comprehensive technical framework that includes theoretical simulations， device fabrication， and experimental validation. The transfer matrix method is utilized to simulate the effects of refractive index modulation depth and grating length on the reflectivity， reflection bandwidth， and effective grating length of the FBG. Through this method， a detailed understanding of the relationship between structural parameters and spectral responses is obtained. Based on the requirements for stable SLM operation， an optimized set of FBG parameters is determined to ensure the efficient operation of the laser around 1053 nm. The simulated high-reflectivity FBG（HR-FBG） achieves a peak reflectivity of 99.94% and a bandwidth of 0.231 nm， while the low-reflectivity FBG（LR-FBG） exhibits a reflectivity of approximately 78.47% and a bandwidth of 0.041 nm. These optimized parameters are crucial for maintaining stable SLM operation and confirming the effectiveness of the simulation methodology in achieving the desired laser performance.Subsequently， a pair of FBG is fabricated based on the optimized parameters for experimental validation. A high-precision wavemeter-based measurement method for characterizing FBG is introduced， offering a significant improvement over conventional methods that utilize broadband femtosecond sources and optical spectrum analyzers（OSA）. The wavemeter-based method achieves a remarkable precision of 0.7 pm for both FBG reflectivity and reflection bandwidth measurements， allowing for the detailed observation of the FBG side-mode lobes， which is crucial for understanding the fine spectral features of the laser. Experimental results show that the traditional OSA-based measurement technique introduces significant errors， especially when determining the 3 dB bandwidth of the LR-FBG. In contrast， the proposed wavemeter-based method offers superior accuracy， with minimal deviation from the simulation results， demonstrating its reliability and precision for FBG characterization.Finally， the characterized FBG pair is fusion-spliced with a 7-mm section of high-gain ytterbium-doped fiber to form a compact DBR resonator， and the performance of the resulting laser is experimentally validated. The laser operates at a center wavelength of 1052.992 nm， with a linewidth of 1.12 kHz， measured over a 100 μs integration time， indicating excellent temporal coherence and stability. Continuous， mode-hop-free tuning of 0.348 nm is achieved by varying the temperature from 3 °C to 55 °C， demonstrating exceptional thermal tuning capability and environmental adaptability. Under a 730 mW pump power at 976 nm， the laser delivers an output power of 41.7 mW， with a side-mode suppression ratio exceeding 75 dB， indicating high spectral purity and effective mode filtering. These results validate the optimized FBG design and the high-performance operation of the DBR SLM fiber laser. This work contributes to the advancement of the design and characterization of FBGs for SLM fiber lasers， significantly improving the accuracy and precision of FBG parameters. While this study focuses on FBG characterization under static， room-temperature conditions， future research will explore the evolution of FBG parameters under varying temperature ranges， dynamic mechanical stress， and exposure to radiation. Additionally， the performance of the laser in practical applications， such as coherent detection， high-precision sensing， and coherent synthesis for high-power laser systems， will be further investigated to fully exploit the potential of SLM fiber lasers in real-world environments.