In order to solve the problem that reduction of the subsequent classification accuracy in the hyperspectral image classification algorithm based on supervised learning due to the presence of noise labels in the training samples, a false label detection algorithm based on low rank sparse representation and improved spectral angle mapping (SAM) was adopted. Firstly, the signal subspace of hyperspectral image was predicted, and the original hyperspectral image was reconstructed and denoised according to the predicted subspace. Next, the normalized spectral angle mapping algorithm was used to obtain the distance information between each class of samples, and the spectral similarity between each class of samples was obtained. Then, the density peak clustering algorithm was used to get the local density of each training sample. Support vector machine was used to verify the results on two real datasets. The experimental results show that the overall accuracy is improved by 1.91% compared with the advanced hierarchical structure of hyperspectral image false label detection algorithm. This result is helpful for hyperspectral image classification.