Conventional index for reliability sensitivity analysis considers only aleatory uncertainty, which cannot show the impacts of epistemic uncertainty in basic variables on structural reliability in the condition of epistemic uncertainty. In view of this, probability boxes are introduced to represent aleatory and epistemic uncertainties in structure, on the basis of which a new index for reliability sensitivity analysis, epistemic sensitivity coefficient, is constructed. The meaning and significance of the new index are explained, and a method based on evidence theory is proposed to calculate it. Numerical examples show that the new coefficient can reveal the contribution of each basic variable to the uncertainty of structural reliability, and it provides a direction to improve the accuracy of reliability calculation. The simulation results also show that the proposed method of epistemic sensitivity calculation is applicable to structures with monotonic as well as non-monotonic limit state equations, and with normal as well as non-normal variables.