Semi-supervised learning and multi-label learning pose different challenges for feature selection, which is one of the core techniques for dimension reduction, and the exploration of reducing feature space for multi-label learning with incomplete label information is far from satisfactory. Existing feature selection approaches devote attention to either of two issues, namely, alleviating negative effects of imperfectly predicted labels and quantitatively evaluating label correlations, exclusively for semi-supervised or multi-label scenarios. A unified framework to extract label correlation information with incomplete prior knowledge and embed this information in feature selection however, is rarely touched. In this paper, we propose a space consistency-based feature selection model to address this issue. Specifically, correlation information in feature space is learned based on the probabilistic neighborhood similarities, and correlation information in label space is optimized by preserving feature-label space consistency. This mechanism contributes to appropriately extracting label information in semi-supervised multi-label learning scenario and effectively employing this information to select discriminative features. An extensive experimental evaluation on real-world data shows the superiority of the proposed approach under various evaluation metrics.