In this article, we propose a marginal robust independence screening procedure based on the entire conditional distribution function of the response. The new method is model-free which dose not require specification of models, and can perform well in the presence of the heavy tails and extreme values in the response. We further show that the proposed method possesses important theoretical properties including ranking consistency property and sure screening property. To reduce the false selection rate, model selection consistency is also be achieved theoretically. We conduct Monte Carlo simulation studies to demonstrate that the proposed methodology exhibits more competitive performance than the existing feature screening methods under different model settings and illustrate the proposed method through a real data analysis.