Variable screening methods have been shown to be effective in dimension reduction under the ultra-high dimensional setting, by giving the optimal feature subset while eliminating the redundant features. Many variable selection techniques for various high-dimensional statistical models have been proposed for linear models and other parametric models. Moreover, although various model-free feature screening methods have been proposed, additional assumptions are imposed to guarantee theoretical results. To address aforementioned obstacles, we develop a new type of variable selection framework for high-dimensional nonparametric regression with two methods called XICOR-SAM and XICOR-penGAM. Our approach combine ideas from sparse additive models(SpAM) and the rank-based coefficient of correlation from Chatterjee(2020) work. We derive a two-stage approach for selecting true important variables in the non-parametric models when the number of covariates is significantly larger than the sample size(p >> n). This framework is capable of capture nonlinear signals and oscillatory trajectory regardless of the distribution of the response. It is shown to enjoy the sure screening property and rank consistency. Extensive simulation studies and real-data analysis demonstrate the effectiveness of the new screening framework. Related R codes can be found here.