Samples are required to meet the manifold assumption in Spectral Embedded Clustering (SEC) algorithm, and class labels of samples can always be embedded in a linear space, which provides a new idea for spectral clustering of linearly separable data, but the linear mapping function used by the spectral embedded clustering algorithm is not available to process the nonlinear high-dimensional data. To solve this problem, this paper cored the linear mapping function, built a Spectral Embedded Clustering based on Kernel function (KSEC) model. This model can solve the problem that the linear mapping function can't deal with nonlinear data, as well as it can achieve kernel's dimension reduction synchronously. The experimental results on real data sets show that the improved algorithm can improve the clustering accuracy by 13.11% averagely, and the highest 31.62%, especially for high-dimensional data clustering accuracy can be increased by 16.53% on average. And the sensitive experiments on algorithm to parameters show the stability of the improved algorithm, so compared with traditional spectral clustering algorithms, higher accuracy and better clustering performance are obtained. And the method can be used for such complex image processing field as remote sensing image.