Similarity matrix is critical to the performance of spectral clustering. Mercer kernels have become popular largely due to its successes in applying kernel methods such as kernel PCA. A novel spectral clustering method is proposed based on local neighborhood in kernel space (SC-LNK), which assumes that each data point can be linearly reconstructed from its neighbors. The SC-LNK algorithm tries to project the data to a feature space by the Mercer kernel, and then learn a sparse matrix using linear reconstruction as the similarity graph for spectral clustering. Experiments have been performed on synthetic and real world data sets and have shown that spectral clustering based on linear reconstruction in kernel space outperforms the conventional spectral clustering and the other two algorithms, especially in real world data sets.