Fourier transform infrared(FTIR) spectrum usually includes a large number of wavelength variables and the qualitative analysis of FTIR spectrum needs to establish a stable and interpretable classification model. Sparse linear discriminant analysis (SLDA), a relatively new and effective machine learning algorithm, is commonly used for variable selection and discriminant analysis of high-dimensional settings, in which the number of wavelength variable is very large and the number of observations is limited. By introducing regularization items into linear discriminant analysis, the classifier training and variable selection are performed simultaneously in SLDA, and the sparsity of load coefficients in different discriminant directions increases the interpretability of the model. A total of 94 samples of Gentiana macrophylla, including 30 Gentiana straminea Maxims, 28 Gentiana officinalis and 36 Gentiana macropylla Pall, were collected. FTIR spectrum of all samples was obtained by Fourier transform infrared spectroscopy method. 70 of the samples were selected as the training set, the remaining as the test set. Based on the training set, the SLDA model was established through the grid optimization of the number of non-zero loading coefficients in the two discriminant directions, and the optimal parameter space was obtained. According to the model parameters, the prediction accuracy of the test set was 100%, and thus the rapid and accurate identification of the three kinds of Gentiana macrophylla was realized. The experimental results showed that the SLDA model was superior to PLS-DA method in terms of classification accuracy, sparseness and interpretability. SLDA will be a novel and effective method for spectroscopy qualitative analysis.