This paper examines the potential of utilizing a Faraday anomalous dispersion optical filter (FADOF) to enhance noise reduction in a FMCW LiDAR (Frequency-Modulated Continuous-Wave Laser Detection And Ranging) system. While the FMCW LiDAR itself demonstrates a certain level of robustness, it may fail to operate effectively in the presence of significant background noise interference. To address this challenge, we have proposed a validation experiment utilizing FADOF technology. Specifically, we have introduced a FADOF component at the optical receiving end of the FMCW LiDAR, and we have implemented a dynamic frequency stabilization method that combines frequency stability with frequency modulation for the laser source in the transmitter. By integrating FADOF into the FMCW LiDAR system to mitigate external noise, we conduct indoor and outdoor validation experiments. In the outdoor experiment, we introduce real sunlight background noise into the system, allowing it to directly illuminate the receiver. We then filter the light using FADOF and a 10 nm filter, separately. The experimental results confirm that the FMCW LiDAR system, when equipped with FADOF, can operate normally in intense background light noise, with a noise resistance capability at least twice as effective as the 10 nm filter. Additionally, the system achieves a detection range of at least 17 meters under direct sunlight conditions. This study has the potential to extend the application of LiDAR systems to more extreme environments with strong background noise, enabling their functionality in a broader range of scenarios.