Convolutional neural networks (CNNs) have demonstrated significant performance in various visual recognition problems in recent years. Recent research has shown that training multilayer neural networks can extensively improve the performance of hyperspectral image (HSI) classification. In this paper, we apply a triplet constraint property on a 3D CNN. This method directly learns a mapping from images to a Euclidean space in which distances directly correspond to a measure of spectral-spatial similarity. Once this embedding has been established, classification can be implemented with such embeddings as feature vectors. Moreover, we also augment the size of the training samples in different band groups. This produces different yet useful estimation of spectral-spatial characteristics of HSI data and contributes considerably in accurate classification. This method is evaluated on a new dataset and compared with several state-of-the-art models, which shows the promising potential of our method.