In this paper, we present a novel Local Sensitive Dual Concept Learning (LSDCL) method for the task of unsupervised feature selection. We first reconstruct the original data matrix by the proposed dual concept learning model, which inherits the merit of co-clustering based dual learning mechanism for more interpretable and compact data reconstruction. We then adopt the local sensitive loss function, which emphasizes more on most similar pairs with small errors to better characterize the local structure of data. In this way, our method can select features with better clustering results by more compact data reconstruction and more faithful local structure preserving. An iterative algorithm with convergence guarantee is also developed to find the optimal solution. We fully investigate the performance improvement by the newly developed terms, individually and simultaneously. Extensive experiments on benchmark datasets further show that LSDCL outperforms many state-of-the-art unsupervised feature selection algorithms.