This paper investigates single relay selection problem for secure communication in a cooperative system with multiple full-duplex decode-and-forward relays, in which an eavesdropper may overhear the source confidential message through relays' transmission. We propose an opportunistic relay selection scheme which selects the relay that maximizes the system secrecy capacity. We then evaluate performance of the proposed scheme in terms of secrecy outage probability. As a comparison, we also derive the secrecy outage probability of the conventional Max-Min relay selection scheme proposed for full-duplex relaying systems without the existence of eavesdroppers. We show that our proposed scheme outperforms the conventional counterpart. Our analytic derivations are also extensively verified by Monte-Carlo simulations.