Existing approaches addressing the few-shot open-set recognition (FSOSR) challenge in hyperspectral images (HSIs) often encounter limitations stemming from sparse labels, restricted category numbers, and low openness. These limitations compromise stability and adaptability. In response, an open-set HSI classification algorithm based on data wandering (DW) is introduced in this research. Firstly, a K-class classifier suitable for a closed set is trained, and its internal encoder is leveraged to extract features and estimate the distribution of known categories. Subsequently, the classifier is fine-tuned based on feature distribution. To address the scarcity of samples, a sample density constraint based on the generative adversarial network (GAN) is employed to generate synthetic samples near the decision boundary. Simultaneously, a mutual-point learning method is incorporated to widen the class distance between known and unknown categories. In addition, a dynamic threshold method based on DW is devised to enhance the open-set performance. By categorizing drifting synthetic samples into known and unknown classes and retraining them together with the known samples, the closed-set classifier is optimized, and a (K + 1)-class open-set classifier is trained. The experimental results in this research demonstrate the superior FSOSR performance of the proposed method across three benchmark HSI datasets.