Femtosecond optical frequency comb, with large spectral range, narrow pulse width, high stability of frequency and many other remarkable properties, has a significant impact on optical frequency metrology, absolute distance measurement and high-precision spectroscopy. The time-domain and frequency-domain properties of femtosecond optical frequency comb is traced back to the microwave frequency standard, making it possible to open up the door to high-precision gas absorption spectrum detection. Femtosecond optical frequency comb spectroscopy has some excellent performances, such as fast measurement, high sensitivity, high resolution, high signal-to-noise ratio and so on. Therefore, more investments on femtosecond optical frequency comb spectroscopy will better make contribution to the environmental protection, industrial production, biological medicine, scientific research and other social fields. High-precision gas absorption spectroscopy with femtosecond optical frequency comb mainly includes frequency comb based cavity ring-down spectroscopy, cavity-enhanced frequency comb spectroscopy and dual-comb multi-heterodyne spectroscopy. Among them, according to the data collection, cavity-enhanced frequency comb spectroscopy can be divided into comb vernier method, virtually imaged phased array method and Fourier transform method. At present, related research has been widely carried out abroad, and domestic research is still in its infancy. This review summarizes main techniques in the high-precision gas absorption spectrum detection based on optical frequency comb, and demonstrates typical experimental schemes for different methods. It also analyzes the advantages and disadvantages of each method, and tracks frontier achievements of main research groups.