Concerning the problems of high-dimensional data, such as non-linearity, low-rank form, and feature redundancy, an unsupervised feature selection algorithm based on kernel function was proposd, named Low Rank Non-linear Feature Selection algroithm (LRNFS). Firstly, the features of each dimension were mapped to a high-dimensional kernel space, and the non-linear feature selection in the low-dimensional space was achieved through the linear feature selection in the kernel space. Then, the deviation terms were introduced into the self-expression form, and the low rank and sparse processing of coefficient matrix were achieved. Finally, the sparse regularization factor of kernel matrix coefficient vector was introduced to implement the feature selection. In the proposed algorithm, the kernel matrix was used to represent its non-linear relationship, the global information of data was taken into account in low rank to perform subspace learning, and the importance of feature was determined by the self-expression form. The experimental results show that, compared with the semi-supervised feature selection algorithm via Rescaled Linear Square Regression (RLSR), the classification accuracy of the proposed algorithm after feature selection is increased by 2.34%. The proposed algorithm can solve the problem that the data is linearly inseparable in the low-dimensional feature space, and improve the accuracy of feature selection.