The spectral clustering is a typical and efficient clustering algorithm. However, the performance of spectral algorithm depends on the determination of the appropriate similarity matrix and the number of clusters. We propose a new spectral clustering algorithm based on fast search of natural neighbors (FSNN-SC) in this paper. In the algorithm, we design a fast search algorithm to obtain the natural characteristic value supk of natural neighbor algorithm in order to improve the efficiency of searching neighbors and to construct a high-quality similarity matrix. At the same time, we design a deep traversal algorithm to adaptively determine the cluster number C. The experimental results verify that our methods are able to improve the search efficiency and find correct number of clusters. The compared experiments show that the accuracy and efficiency of the proposed algorithm are better than others.