The advantages of fiber optic sensors based on fiber optic interferometers with explosion-proof safety in gas pipeline monitoring has gradually emerged. A monitoring system for natural gas pipelines was designed and implemented using a Michelson interferometer as the core structure of the fiber optic sensor and processed the collected data using phase carrier generation demodulation algorithms. Addressing practical issues such as phase wrapping and arm length difference losses, an improved phase carrier demodulation algorithm based on tangent transformation and arctangent-differential self-cross-multiplication was proposed. Field experiments were conducted in gas valve chambers, to analyze the characteristics of leak signals in the pipeline. This study lays the foundation for the application of fiber optic interferometer sensors in gas pipeline monitoring, promising enhanced safety and efficiency.