Continuously high-speed spectroscopic gas detection with a wide spectral span has a long time been a challenge. We propose a method based on an extended optical linear chirp chain (EOLCC) for gas spectrum measurement with a fast acquisition rate and a broad bandwidth. The basic optical linear chirp (OLC) unit moves a fixed frequency when it passes through an optical loop containing a dual-parallel Mach-Zehnder modulator driven by a microwave signal. This method is demonstrated by monitoring a high-speed flow process of acetylene gas under normal pressure, achieving a spectral bandwidth of 88 GHz, a repetition frequency of 0.53 MHz, a 100% duty cycle, and a frequency-chirping linearity error of 5.2 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> . Our proposed method based on the EOLCC is expected to have a repetition frequency on the MHz order, showing great potential in the development of high speed optical gas sensors.