Local geometric structure Fisher analysis (LGSFA) utilizes neighbor points and corresponding reconstructions to determine the intrinsic manifold structure of hyperspectral data, and it can improve the classification accuracy of hyperspectral image (HSI). However, LGSFA uses original sample and reconstruction points to construct graphs together, which cannot effectively preserve the global structure of nonlinear manifolds in low-dimensional spaces. To address this issue, this paper proposes a local reconstruction Fisher analysis (LRFA) method for HSI classification. The proposed method first reconstructs each data point from its intraclass neighbors to learn the global structure of manifolds. Then, intrinsic graph and penalty graph are constructed based on these reconstructions. In the low-dimensional space, the intraclass compactness and the interclass separability are improved by minimizing the intraclass distance and maximizing the interclass distance, respectively. Thus, the distinction in features is enhanced for HSI classification. Experimental results on the Pavia University and Urban datasets prove the effectiveness of the proposed method. Compared with other state-of-art methods, the proposed method achieves higher classification accuracy. When 1% of samples are randomly selected for training, the overall accuracy of 86.07% and 83.77% are obtained and increased by 7.84 percentage points and 1.27 percentage points, respectively, in comparison with the results of LGSFA.