Owing to the general disadvantages of traditional neural networks in gas concentration inversion, such as slow training speed, sensitive learning rate selection, unstable solutions, weak generalization ability, and an ability to easily fall into local minimum points, the extreme learning machine (ELM) was applied to sulfur hexafluoride (SF6) concentration inversion research. To solve the problems of high dimensionality, collinearity, and noise of the spectral data input to the ELM network, a genetic algorithm was used to obtain fewer but critical spectral data. This was used as an input variable to achieve a genetic algorithm joint extreme learning machine (GA-ELM) whose performance was compared with the genetic algorithm joint backpropagation (GA-BP) neural network algorithm to verify its effectiveness. The experiment used 60 groups of SF6 gas samples with different concentrations, made via a self-developed Fourier transform infrared spectroscopy instrument. The SF6 gas samples were placed in an open optical path to obtain infrared interference signals, and then spectral restoration was performed. Fifty groups were randomly selected as training samples, and 10 groups were used as test samples. The BP neural network and ELM algorithms were used to invert the SF6 gas concentration of the mixed absorbance spectrum, and the results of the two algorithms were compared. The sample mean square error decreased from 248.6917 to 63.0359; the coefficient of determination increased from 0.9941 to 0.9984; and the single running time decreased from 0.0773 to 0.0042 s. Comparing the optimized GA-ELM algorithm with traditional algorithms such as ELM and partial least squares, the GA-ELM algorithm had higher prediction accuracy and operating efficiency and better stability and generalization performance in the quantitative analysis of small samples of gas under complex noise backgrounds.