Linear discriminant analysis (LDA) is a popular technique for supervised dimensionality reduction, but with less concern about a local data structure. This makes LDA inapplicable to many real-world situations, such as hyperspectral image (HSI) classification. In this letter, we propose a novel dimensionality reduction algorithm, locality adaptive discriminant analysis (LADA) for HSI classification. The proposed algorithm aims to learn a representative subspace of data, and focuses on the data points with close relationship in spectral and spatial domains. An intuitive motivation is that data points of the same class have similar spectral feature and the data points among spatial neighborhood are usually associated with the same class. Compared with traditional LDA and its variants, LADA is able to adaptively exploit the local manifold structure of data. Experiments carried out on several real hyperspectral data sets demonstrate the effectiveness of the proposed method.