Hyperspectral image (HSI) generally contains a complex manifold structure and strong sparse correlation in its nonlinear high-dimensional data space. However, the existing manifold learning and sparse learning methods usually consider the manifold structure and sparse relationship separately rather than combining manifold and sparse properties to discover the intrinsic information in the original data. To simultaneously reveal the complex sparse relation and manifold structure of HSI, a novel feature extraction (FE) method, called local manifold-based sparse discriminant learning (LMSDL), has been proposed on the basis of manifold learning and sparse representation (SR). The LMSDL method first designs a new sparse optimization model called local manifold-based SR (LMSR) to reveal the local manifold-based sparse structure of data. Then, two geometrical sparse graphs are constructed to represent the discriminant relationship between samples and the geometrical and sparse neighbors. An objective function is constructed via geometrical sparse graphs and reconstruction points to learn a projection matrix for FE. The LMSDL effectively reveals the complex sparse relation and manifold structure in high-dimensional data, and it enhances the representation ability of extracted features for HSI classification significantly. The experimental results on the three real HSI datasets show that the proposed LMSDL algorithm possesses better performance in comparison with some state-of-the-art FE methods.