In order to solve the “dimension disaster” problem caused by high-dimensional data classification, the paper proposes a new feature selection algorithm combining kernel function with sparse learning. Specifically, the kernel function is firstly used to map every dimensional feature to the kernel space, and linear feature selection is performed in the high dimensional kernel space to achieve nonlinear feature selection in the low dimensional space. Secondly, sparse reconstruction is performed on the features mapped to the kernel space, so as to gain a sparse representation of the original dataset. Next, L1-norm is used to construct a feature selection mechanism and selects the optimal feature subset. Finally, the data after the feature selection is used in the classification experiments. Experimental results on public datasets show that, compared with the comparison algorithm, the proposed algorithm can conduct the feature selection better and improve the classification accuracy by about 3%.