Hyperspectral image (HSI) classification is an active research topic in remote sensing. Supervised learning-based methods have been widely used in HSI classification tasks due to their powerful feature extraction capabilities for cases of sufficiently labeled samples. However, practical applications often have limited samples with accurate labels due to the high cost of labeling or unreliable visual interpretation. We introduce a contrastive self-supervised learning (SSL) algorithm to achieve HSI classification for problems with few labeled samples. First, a new HSI-specific augmentation module is developed to generate sample pairs. Then, a contrastive SSL model based on Siamese networks is used to extract features from these easily accessible sample pairs. Finally, the labeled samples are taken to fine-tune the parameters of the classification model to boost classification performance. Tests of the contrastive self-supervised algorithm have been performed on two widely used HSI datasets. The experimental results reveal that the proposed algorithm requires a few labeled samples to achieve superior performance.