Based on spectral partition theory, spectral clustering algorithms are effective to solve the clustering of arbitrary sphere of sample spaces, and they can converge to global optimal solution. However, spectral clustering algorithms have to adopt the appropriate scaling parameter to calculate the whole similarity matrix, which may have a great impact on the clustering results. Moreover, when the number of data instances is large, computational complexity and memory use of the algorithm will greatly increase. So, we propose a fast algorithm for adaptive spectral clustering based on K-nearest neighbors, which can choose the scaling parameter automatically. Meantime, we divide the data set into different blocks and compute it separately. We also construct sparse matrix via retaining nearest neighbors to overcome the computational and the memory difficulties. Compared with traditional spectral clustering algorithms, experimental results show this algorithm can achieve better clustering effect on artificial datasets and UCI public databases.