We propose a model-free variable selection approach, i.e., constrained kernel regression (CONKER). Instead of relying on model-based loss functions, the proposed CONKER approach is developed based on the conditional independence relationship measured by the conditional distance covariance/correlation. The conditional distance covariance/correlation is further approximated using the kernel density estimation method. The CONKER coefficient vector is then defined to be the vector satisfying the approximated conditional independence constraints. The proposed approach provides a solution path by varying the tuning parameter in the conditional independence constraints. We prove that the proposed CONKER approach can consistently identify the true important predictor set under high-dimensional model-free settings with appropriate tuning parameters. We further develop a data-driven approach to select the tuning parameter of the proposed approach. The advantage of the proposed procedure is further shown by various numerical studies. More specifically, the proposed model-free procedure surpasses the existing model-based methods in the presence of model misspecification while outperforming or at least equating to the existing ones with correctly specified models.