In this paper, we use the terahertz time-domain spectroscopy system to measure the terahertz absorption spectra of three common food additives, namely, benzoic acid, sorbic acid, and xylitol, along with their mixtures. In addition, we select three machine learning algorithms to analyze the binary and ternary mixtures of food additives, namely, the partial least squares regression (PLS), the least squares support vector machine (LS-SVM), and the backpropagation neural network (BPNN). We find that in the quantitative analysis of multivariate mixtures, the nonlinear models LS-SVM and BPNN are more advantageous than the linear model PLS. As the mixture composition increased, the advantages of using a nonlinear model for analysis become more obvious. Among the two nonlinear models, we find that LS-SVM has a fixed modeling step compared with that of BPNN and does not require complicated parameter discussion and optimization, which can efficiently realize the quantitative analysis of multivariate mixtures. Moreover, by observing the spectral characteristics of the analyte, it is found that in addition to the discussion of the applicability of the algorithm, the spectral characteristics of the analyte also affect the accuracy of quantitative detection to a certain extent.