Hyperspectral image classification is a challenging and significant domain in the field of remote sensing with numerous applications in agriculture, environmental science, mineralogy, and surveillance. In the past years, a growing number of advanced hyperspectral remote sensing image classification techniques based on manifold learning, sparse representation and deep learning have been proposed and reported a good performance in accuracy and efficiency on state-of-the-art public datasets. However, most existing methods still face challenges in dealing with large-scale hyperspectral image datasets due to their high computational complexity. In this work, we propose an improved spectral clustering method for large-scale hyperspectral image classification without any prior information. The proposed algorithm introduces two efficient approximation techniques based on Nyström extension and anchor-based graph to construct the affinity matrix. We also propose an effective solution to solve the eigenvalue decomposition problem by multiplicative update optimization. Experiments on both the synthetic datasets and the hyperspectral image datasets were conducted to demonstrate the efficiency and effectiveness of the proposed algorithm.