Most existing feature selection methods in literature are linear models, so that the nonlinear relations between features and response variables are not considered. Meanwhile, in these feature selection models, the interactions between features are often ignored or just discussed under prior structure information. To address these challenging issues, we consider the problem of sparse additive models for high-dimensional nonparametric regression with the allowance of the flexible interactions between features. A new method, called as sparse shrunk additive models (SSAM), is proposed to explore the structure information among features. This method bridges sparse kernel regression and sparse feature selection. Theoretical results on the convergence rate and sparsity characteristics of SSAM are established by the novel analysis techniques with integral operator and concentration estimate. In particular, our algorithm and theoretical analysis only require the component functions to be continuous and bounded, which are not necessary to be in reproducing kernel Hilbert spaces. Experiments on both synthetic and real-world data demonstrate the effectiveness of the proposed approach.