Oxygen is an essential component of the engine combustion process. It is an urgent demand for aircraft inlet oxygen monitoring. Aiming at aircraft engineering requirements and application characteristics, a short-path wavelength linear scanning tunable diode laser absorption spectroscopy (TDLAS) system is designed, which complete the weak oxygen absorption signal extraction and concentration inversion combined with the second derivative spectrum algorithm based on finite impulse response (FIR) filter. Theoretical basis for the second derivative spectrum method of gas concentration inversion is deduced according to the absorption signal characteristics and the TDLAS principle. A solution based on the FIR digital filter to complete absorption signal noise filtering and second derivative spectrum extracting is proposed on this basis. Experimental results show that this scheme is simple, the detected signal to noise ratio is improved, and the detection limit is reduced. Inversion results of gas concentration are accurate and linearity is good.