In order to deal with the case where the terahertz spectrums are linearly inseparable, this paper proposes a method combining the radial basis function and the kernel principal component analysis (KPCA) to extract the terahertz spectral features of edible oils. By using this method, the extracted inner-class distance of features is small, meanwhile the extracted inter-class distance is large. An accurate classification model can be established in most support vector machine classifiers. Terahertz spectroscopy is an important method to detect the type and quality of edible oils. The research on the feature extraction technology of terahertz spectroscopy is of great significance for the rapid detection of edible oil types and quality. Although there have been a theoretical basis on how to use the terahertz spectroscopy to detect the type and quality of edible oils, it is still difficult to accurately extract the terahertz spectral features of edible oils and establish an accurate classification mode accordingly. Recently, researchers often use principal component analysis (PCA) in the field of chemometrics to extract features and use machine learning algorithms to establish a material classification model. However, the linear separability of the terahertz spectrum of edible oils has different characteristics in different frequency bands. When the terahertz spectrums of edible oils are linearly separable, it is feasible to extract features using PCA, and thus establish an accurate classification model. However, when the terahertz spectrums of edible oils are linearly inseparable, the features extracted using PCA are often not accurate enough, and an appropriate classifier is demanded to establish an accurate classification model. The method combining the radial basis function and KPCA feature extraction can be described as follows: the linear space-inseparable terahertz spectral data are mapped to the radial basis space by the radial basis function, then the features are extracted by KPCA which become linearly separable. As a result, a more accurate classification model can be established. For the experiment, firstly the sliding window average filtering algorithm is used to filter the terahertz spectral data of three edible oils. Then, the radial basis function is employed to nonlinearly map the terahertz spectrum. After that, KPCA is utilized for data dimensionality reduction. Finally, the support vector machine (SVM) is used to establish a classification model for edible oils and the feature extraction effect is verified. The calculated results of inter-class separability show that the inner-class distance of features extracted by the method is smaller, and the inter-class distance is larger. Thus, the overall feature extraction effect presented in this paper is better than those of PCA and KPCA. The experimental results of classification verification show that based on certain classification models the features extracted by PCA and KPCA cannot distinguish the type of edible oils very accurately. However, based on every classification model the feature extraction method proposed in this paper can distinguish the type of edible oils accurately. The method proposed in this paper has a better effect on the extraction of terahertz spectral features of edible oils, which makes it of great value in the detection and analysis of the quality of edible oils.