This letter investigates the physical layer security for a buffer-aided underlay cooperative cognitive radio network in the presence of an eavesdropper, wherein, the relay is equipped with a buffer so that it can store packets received from the secondary source. To improve the secure performance of cognitive radio networks, we propose a novel cognitive secure link selection scheme which incorporates the instantaneous strength of the wireless links as well as the status of relay's buffer, the proposed scheme adapts the link selection decision on the strongest available link by dynamically switching between relay reception and transmission. Closed-form expressions of secrecy outage probability (SOP) for cognitive radio network is obtained based on the Markov chain. Numerical results demonstrate that the proposed scheme can significantly enhance the secure performance compared to the conventional relay selection scheme.