Recently, broad learning system (BLS) has been widely used in hyperspectral image (HSI) classification with its excellent learning performance and generalization ability. However, BLS only focuses on the separability of various samples, ignoring the relative relationship between samples and the discriminative information. To some extent, it limits the performance of BLS. Therefore, we propose a local sensitive discriminative broad learning system (LSDBLS) for HSI classification. LSDBLS considers the discriminative information of labeled samples and the local manifold structure of data samples by introducing local sensitive discriminant analysis, and construct intra-class and inter-class graphs by labeled samples to representation the relative relationship between data samples. On this basis, the intra-class graph and the inter-class graph are introduced into the objective function of the broad learning system. By minimizing the intra-class graph and maximizing the inter-class graph, the samples of the same class are aggregated as much as possible, and the samples of different classes are as much as possible, so as to enhances the discriminative ability of LSDBLS for data features. Experimental results on three HSI datasets show that LSDBLS achieves good performance.