In this paper, we present an integrated framework for quantifying epistemic uncertainty in probabilistic risk assessment. Three types of epistemic uncertainty, that is, completeness, structural and parametric uncertainties, are considered. A maturity model is developed to evaluate the management of these epistemic uncertainties in the model building process. The impact of epistemic uncertainty on the result of the risk assessment is, then, estimated based on the developed maturity model. Then, an integrated risk index is defined to reflect the epistemic uncertainty in the risk assessment results. An indifference method is developed to evaluate the index based on the maturity of epistemic uncertainty management. A case study concerning a nuclear power plant is shown to demonstrate the applicability of the overall modelling framework.