In recent years, different deep learning frameworks were introduced for hyperspectral image (HSI) classification. However, the proposed network models have a higher model complexity, and do not provide high classification accuracy if few-shot learning is used. This paper presents an HSI classification method that combines random patches network (RPNet) and recursive filtering (RF) to obtain informative deep features. The proposed method first convolves image bands with random patches to extract multi-level deep RPNet features. Thereafter, the RPNet feature set is subjected to dimension reduction through principal component analysis (PCA), and the extracted components are filtered using the RF procedure. Finally, the HSI spectral features and the obtained RPNet-RF features are combined to classify the HSI using a support vector machine (SVM) classifier. In order to test the performance of the proposed RPNet-RF method, some experiments were performed on three widely known datasets using a few training samples for each class, and classification results were compared with those obtained by other advanced HSI classification methods adopted for small training samples. The comparison showed that the RPNet-RF classification is characterized by higher values of such evaluation metrics as overall accuracy and Kappa coefficient.