An N-k contingencies risk analysis method of power grid with multi-mode hidden failure in the relay protection system taken into account is proposed.A hidden failure model is developed for the relay protection system that takes into account the hidden failure of line main protection，backup protection and breaker（failure to act）.A method based on function group and event tree analysis is used to calculate the probability of N-k failure，and an integrated consequent loss index is proposed which includes independent power，load loss and decline of the limit of transmission sections.The results show that compared with the method considering a single hidden failure mode，the proposed method can improve the calculating accuracy of N-k failure probability，identify some special high risk N-k failure paths，and find out weak links in the relay protection system.