Hyperspectral image (HSI) classification methods have made great progress in recent years. However, most of these methods are rooted in the closed-set assumption that the class distribution in the training and testing stages is consistent, which cannot handle the unknown class in open-world scenes. In this work, we propose a feature consistency-based prototype network (FCPN) for open-set HSI classification, which is composed of three steps. First, a three-layer convolutional network is designed to extract the discriminative features, where a contrastive clustering module is introduced to enhance the discrimination. Then, the extracted features are used to construct a scalable prototype set. Finally, a prototype-guided open-set module (POSM) is proposed to identify the known samples and unknown samples. Extensive experiments reveal that our method achieves remarkable classification performance over other state-of-the-art classification techniques.