Semi-supervised learning (SSL) methods assume that labeled data, unlabeled data and test data are from the same distribution. Open-set semi-supervised learning (Open-set SSL) considers a more practical scenario, where unlabeled data and test data contain new categories (outliers) not observed in labeled data (inliers). Most previous works focused on outlier detection via binary classifiers, which suffer from insufficient scalability and inability to distinguish different types of uncertainty. In this paper, we propose a novel framework, Adaptive Negative Evidential Deep Learning (ANEDL) to tackle these limitations. Concretely, we first introduce evidential deep learning (EDL) as an outlier detector to quantify different types of uncertainty, and design different uncertainty metrics for self-training and inference. Furthermore, we propose a novel adaptive negative optimization strategy, making EDL more tailored to the unlabeled dataset containing both inliers and outliers. As demonstrated empirically, our proposed method outperforms existing state-of-the-art methods across four datasets.