Cross-domain methods have been proposed to learn the domain invariant knowledge that can be transferred from the source domain to the target domain. Existing cross-domain methods attempt to minimize the distribution discrepancy of the domains. However, these methods fail to explore the domain invariant subspace due to the samples of different classes between two domains may overlap in the new subspace. They consider the features in the original space data that may be unnecessary or irrelevant to the final classification, and neglect to preserve the local manifold structure between two domains. To solve these problems, a novel feature extraction method called Locality Cross-domain Discriminant Analysis (LCDA) is proposed. LCDA first aligns the distributions and avoids overlap between two domains. Then, LCDA exploits the local manifold structure to maintain the discriminative capability of the low-dimensional projection matrices. Finally, a robust constraint is utilized to preserve the robustness of the projection matrices. The proposed LCDA not only avoids overlap between different classes but also explores the local manifold information. Experiment results on the medical membranous nephropathy hyperspectral dataset demonstrate that the proposed LCDA has better performance than other relevant feature extraction methods.