Wheat yellow rust is one of the most destructive diseases in wheat production and significantly affects wheat quality and yield. Accurate and non-destructive identification of yellow rust is critical to wheat production management. Hyperspectral imaging technology has proven to be effective in identifying plant diseases. We investigated the feasibility of identifying yellow rust on wheat leaves using spectral features and textural features (TFs) of hyperspectral images. First, the hyperspectral images were preprocessed, and healthy and yellow rust-infected samples were obtained by creating regions of interest. Second, the extraction of spectral reflectance characteristics and vegetation indices (VIs) were performed from the preprocessed hyperspectral images, and the TFs were extracted using the grey-level co-occurrence matrix from the images transformed by principal component analysis. Third, the successive projections algorithm was employed to choose the optimum wavebands (OWs), and correlation-based feature selection was employed to select the optimal VIs and TFs (those most sensitive to yellow rust and having minimal redundancy between features). Finally, identification models of wheat yellow rust were established using a support vector machine and different features. Six OWs (538, 598, 689, 702, 751, and 895 nm), four VIs (nitrogen reflectance index, photochemical reflectance index, greenness index, and anthocyanin reflectance index), and four TFs (correlation 1, correlation 2, entropy 2, and second moment 3) were selected. The identification models based on the OWs, VIs, and TFs provided overall accuracies of 83.3%, 89.5%, and 86.5%, respectively. The TF results were especially encouraging. The models with the combination of spectral features and TFs exhibited better performance than those using the spectral features or TFs alone. The accuracies of the models with the combined features (OWs and TFs, Vis, and TFs) were 90.6% and 95.8%, respectively. These values were 7.3% and 6.3% higher, respectively, than those of the models using only the OWs or VIs. The model with the combined feature (VIs and TFs) had the highest accuracy (95.8%) and was used to map the yellow rust lesions on wheat leaves with different damage levels. The results showed that the yellow rust lesions on the leaves could be identified accurately. Overall, the combination of spectral features and TFs of hyperspectral images significantly improved the identification accuracy of wheat yellow rust.