A new secure transmission scheme is proposed for the communication security of a Successive Relaying（SR） network with multiple eavesdroppers and multiple relays. In order to minimize the average Secrecy Outage Probability（SOP） of the system, at each time slot for the confidential signal transmitting from the source, one best relay is selected to successively forward the signals of the previous slot to interfere with the eavesdropping. Meanwhile interference cancellation is performed at the destination. For performance analysis, the closed-form expression of the average SOP is derived. Simulation results confirm the proposed theoretical results on the average SOP, and reveal that the proposed scheme can significantly decrease the SOP compared with the traditional ways.