In order to predict the extreme value of nonlinear vibration response of stay cable under random vehicle load. Firstly，Monte-Carlo random sampling method is used to generate random traffic flow load， and the displacement of stay cable beam end and tower end under random traffic flow load is solved. Then， the vehicle induced displacement at the beam end and tower end of the stay cable is taken as the external excitation input of the stay cable， and the nonlinear spatial coupling vibration response of the stay cable is solved by Runge-Kutta numerical method. Finally， based on the extreme value prediction theory of classical rice formula， an extreme value prediction method of nonlinear vibration response of stay cable under random vehicle excitation is proposed. The practical engineering application results show that the vehicle load provides a large vertical and longitudinal displacement excitation for the beam end of the cable， and a large longitudinal displacement excitation for the tower end， which has a great influence on the axial and in-plane vibration response of the cable， and a small influence on the out-of-plane vibration response of the cable. The extremum of vehicle-induced vibration response of stay cable increases with the increase of traffic density and recurrence period. The classical Rice formula has a good fitting effect on the threshold crossing times of vehicle-induced vibration response limit of stay cable. The prediction method of extreme value of nonlinear vibration response of stay cable proposed in this paper is effective， reliable and convenient to be applied in engineering practice.