Abstract: Both aleatory uncertainty and epistemic uncertainty exist in the initial and boundary conditions when we numerically solve the CFD with sharp discontinuity. In this paper, mixed uncertainty quantification approaches are developed to deal with this situation. Specifically, the outer level uncertainty is linked to epistemic uncertainties, and the inner uncertainty is linked to aleatory uncertainty. The non-intrusive polynomial chaos method is utilized to cope with the aleatory uncertainties, while the P-box theory is used to deal with the epistemic uncertainties, and the upwind scheme and Riemann solver are used to solve the deterministic system. We apply this method to the Sod problem in the CFD, and acquire preferable effect. This method evaluates the influence of input uncertainty such as density (aleatory uncertainty) and polytrophic exponent (epistemic uncertainty) on the output uncertainty, the efficiency of this method is also proved. This method is also helpful in evaluating the degree of confidence and validation of the result from modeling and simulation by other models.