The airborne electronic systems of civil aircraft exhibit complex and comprehensive characteristics, and common cause failures will undermine the independence of failure events in the system, which may lead to deviations in the results of quantitative safety assessment. Aiming at the current problem of analyzing common cause failures by qualitative methods in the field of civil aircraft, which relies heavily on the engineering experience of the evaluators, a failure probability algorithm for complex airborne electronic systems considering common cause failure is proposed. Firstly, an Alpha factor model is used to quantify the common cause failures. Then, it is integrated into the fault tree model based on the independence assumption to optimize it. Finally, taking the failure state of a typical complex airborne electronic system as an example, the failure probability with or without common cause failure is compared with each other. The results show that the common cause failure will have two orders of magnitude error influence on the quantitative safety evaluation results of complex airborne electronic systems, and the proposed method can quantify the common cause failure problem, which may provide a technical support for the further application of complex airborne electronic system of civil aircraft.