Linear discriminant analysis (LDA) is one of the most successful feature extraction methods, which projects high-dimensional data to a low-dimensional space with discriminative features. However, there are problems in the existing LDAs: (1) the effect of hidden data is not exploited in LDA, (2) the LDAs cannot preserve the local isometric structure, (3) there is no consideration for structural consistency that unifies the supervised global and unsupervised local information. In this paper, we propose a brand-new LDA method, namely, Latent Linear Discriminant Analysis with Isometric Structural Learning (LDA-ISL). We formulate LDA to a latent representation framework that considers both the discriminability from observed data and hidden data. Then, we propose isometric structural learning to capture the intrinsic local structural information. Lastly, we establish the concept of structural consistency in LDA framework. Extensive experiments and comparisons show that LDA-ISL achieves a promising performance with structural consistency and stronger robustness in feature extraction.