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In this paper, we investigate the physical layer security of a dual-hop cooperative network in the presence of a full-duplex active eavesdropper, which can overhear the confidential signals and transmit jamming signals simultaneously. We utilize the optimal relay selection scheme to improve the secrecy performance, where the relay maximizing the secrecy capacity will be selected to forward the information. To evaluate the secrecy performance of our system, we derive a compact closed-form expression of the secrecy outage probability. Besides, we also analyze the asymptotic performance related to the position of the nodes. Finally, we verify our analysis through the numerical results, and demonstrate that there exists a secrecy protection region where the secrecy outage probability is below a target probability.