In this paper, the secrecy performance of a cooperative relay network with outdated relay selection is investigated where an eavesdropper intercepts the channels between the source and the destination. The best relay is chosen among N relays based on the opportunistic relay selection algorithm, which may not be the best relay at the time of transmission because of the outdated channel state information. We derive closed-form analytical expressions for the non-zero secrecy capacity, the secrecy outage probability, and the ergodic secrecy capacity. Finally, our theoretical analysis is validated by the numerical results, and detailed discussions and insights are given.