Given the detrimental effect of spectral variations in a hyperspectral image (HSI), this paper investigates to recover its discriminative representation to improve the classification performance. We propose a new method, namely local low-rank approximation with superpixel-guided locality preserving graph (LLRA-SLPG), which can reduce the spectral variations and preserve the local manifold structure of an HSI. Specifically, the LLRA-SLPG method first clusters pixels of an HSI into several groups (i.e., superpixels). By taking advantage of the local manifold structure, a Laplacian graph is constructed from the superpixels to ensure that a typical pixel should be similar to its neighbors within the same superpixel. The LLRA-SLPG model can increase the compactness of pixels belonging to the same class by reducing spectral variations while promoting local consistency via the Laplacian graph. The objective function of the LLRA-SLPG model can be solved efficiently in an iterative manner. Experimental results on four benchmark datasets validate the superiority of the LLRA-SLPG model over state-of-the-art methods, particularly in cases where only extremely few training pixels are available.