An efficient system reliability analysis method with a parametric probability box （p-box） model is proposed to solve the problem that the mixture of aleatory and epistemic uncertainty exists in mechanical systems. Firstly， the minimum reliability index of the single failure mode is obtained based on the sequential iteration decoupling method. Then， aiming at the multiple failure modes problem under the mixture of aleatory and epistemic uncertainty， the system reliability analysis model is established based on the parametric p-box uncertainty. Considering the correlation among the failure modes， the correlation coefficient matrix between each failure mode is calculated by the linear correlation degree analysis method. Finally， a reliability calculation method for both series and parallel systems is proposed， which has high reliability calculation efficiency and can meet the practical engineering requirements compared with the traditional double-loop Monte Carlo sampling method.