Sensitivity Analysis （SA） can identify the most important parameters affecting the complex system output to support robust design of a system. Non-parametric probability-box （P-box）， as a typical imprecise probabilistic model， can effectively quantify both aleatory and epistemic uncertainties， therefore extensively used in engineering practices. As aleatory and epistemic uncertainties are coupled in P-boxes， sensitivity analysis under the P-box framework is essential to evaluate their contributions in input P-box variables to output. This study develops a Separating Sensitivity Analysis （SSA） method for aleatory and epistemic uncertainties of non-parametric p-boxes. Two methods， i.e.， grid point method and expectation method， are introduced to separate the input aleatory and epistemic uncertainties in input P-box variables， respectively. A double loop procedure is utilized to propagate the input uncertainties and build the output P-box. Two uncertainty measures， namely， maximum variance metric and area metric， are proposed to evaluate the effects of input aleatory and epistemic uncertainties on the output aleatory and epistemic uncertainties， respectively. The lift-to-drag ratio prediction of the NACA0012 airfoil is exemplified to analyze the contributions of aleatory and epistemic uncertainties of income flow parameters and turbulence model parameters to those of the lift-to-drag ratio prediction result.