In order to meet the needs of accurate, fast and portable measurement of greenhouse gases such as CO₂ and CH₄, a multi-wavelength greenhouse gas measurement system based on tunable Fabry-Perot interferometer (FPI) sensor is introduced in this paper. Using FPI as wavelength selective element, the continuous measurement in band of 3100--4400 nm (wavenumber range is 3226--2273 cm ^-1) is realized through interference filter. The correlation coefficient is obtained by fitting the measured absorption spectrum with the absorption cross section of CO₂, and then the gas concentration of CO₂ can be calculated. To correct the non-linear absorption effect that caused by the low resolution of the instrument, the iterative algorithm is used to optimize the CO₂ absorption cross section. The results show that the measurement error is reduced by 18% compared with the direct fitting calculation when concentration of CO₂ is 4.08×10 ^-4. The interference optimization, precision, the limit of detection and other parameters of the system are verified. The experimental results show that the concentration of residual CO₂ in the air chamber is less than 1×10 ^-6, the instrument precision is ±1.32×10 ^-6, and the detection limit is 1.13×10 ^-6 (2σ, 2 times standard deviation) when the time resolution is 10 minutes. Moreover, the system is used to carry out outdoor measurement in Hefei Science Island for one week, and the daily variation results and diurnal characteristics of concentrations of CO₂ are obtained, which verified the stability and reliability of the system.