In multi-label learning, each training instance is associated with multiple labels simultaneously. Traditional multi-label learning studies primarily focus on closed set scenario, i.e. the class label set of test data is identical to those used in training phase. Nevertheless, in numerous real-world scenarios, the environment is open and dynamic where unknown labels may emerge gradually during testing. In this paper, the problem of multi-label open set recognition (MLOSR) is investigated, which poses significant challenges in classifying and recognizing instances with unknown labels in multi-label setting. To enable open set multi-label prediction, a novel approach named SLAN is proposed by leveraging sub-labeling information enriched by structural information in the feature space. Accordingly, unknown labels are recognized by differentiating the sub-labeling information from holistic supervision. Experimental results on various datasets validate the effectiveness of the proposed approach in dealing with the MLOSR problem.