Feature selection plays an important role to select the informative and valuable features especially in high-dimensional data. However, some conventional feature selection methods select the features according to a feature subset score, which are often time-consuming, not quite robust to noise and neglecting the local data structure. To address this problem, we propose a novel feature selection approach, namely locality-based discriminant feature selection with trace ratio (LDFS), which can perform local data structure learning, and feature selection simultaneously. Furthermore, the proposed approach is robust to data noise and can pick out genuinely valuable features. In the end, experimental results on synthetic and real-world datasets demonstrate the effectiveness of the proposed method. © 2018 IEEE.