In this paper, we formulate a new research problem of learning from vaguely labeled one-class data streams, where the main objective is to allow users to label instance groups, instead of single instances, as positive samples for learning. The batch-labeling, however, raises serious issues because labeled groups may contain non-positive samples, and users may change their labeling interests at any time. To solve this problem, we propose a Vague One-Class Learning (VOCL) framework which employs a double weighting approach, at both instance and classifier levels, to build an ensembling framework for learning. At instance level, both local and global filterings are considered for instance weight adjustment. Two solutions are proposed to take instance weight values into the classifier training process. At classifier level, a weight value is assigned to each classifier of the ensemble to ensure that learning can quickly adapt to users’ interests. Experimental results on synthetic and real-world data streams demonstrate that the proposed VOCL framework significantly outperforms other methods for vaguely labeled one-class data streams.