Domain adaptation is a proven hyperspectral image (HSI) classification approach aimed at transferring knowledge from a label-rich domain to a label-scarce domain. Existing literature assumes a closed-set scenario in which both the source and target domains share exactly the same label space (“known classes”). However, this assumption may be too ideal in practice. Often, the target domain contains private classes unknown to the source (“unknown classes”). It requires domain adaptation methods to classify the known classes accurately while simultaneously rejecting unknown classes. Focusing on the open-set setting, this paper creatively proposes a hyperspectral open set domain adaptation model based on adversarial learning with a three-dimensional convolutional neural network as the feature extractor, which can sufficiently explore joint spatial-spectral information of HSI and improve classification performance significantly. In addition, this model introduces a dynamic weighting scheme based on multiple auxiliary classifiers for inhibiting negative transfers during adversarial training. Experiment results on three benchmark hyperspectral datasets verify the superiority of the proposed approach for the hyperspectral open set classification. Compared with state-of-the-art techniques with and without using target samples during training, the proposed method improves the mean AUC values by at least 0.157, 0.028, and 0.163 on the Pavia University, Pavia Centre, and Indian Pines datasets, respectively.