Feature selection plays an important role in pattern recognition and machine learning systems. Supervised knowledge can significantly improve the performance. However, confronted with the rapid growth of newly-emerging concepts, existing supervised methods may easily suffer from the scarcity of labeled data for training. Therefore, this paper studies the problem of Zero-Shot Feature Selection, i.e., building a feature selection model that generalizes well to "unseen" concepts with limited training data of "seen" concepts. To address this, inspired by zero-shot learning, we use class-semantic descriptions (i.e., attributes) which provide additional semantic information about unseen concepts as supervision. In addition, to seek for more reliable discriminative features, we further propose a novel loss function (named center-characteristic loss) which encourages the selected features to capture the central characteristics of seen concepts. Experimental results on three benchmarks demonstrate the superiority of the proposed method.