This paper investigates data transmission and physical layer secrecy in cognitive radio network. We propose to apply full duplex transmission and dual antenna selection at secondary destination node. With the full duplex transmission, the secondary destination node can simultaneously apply the receiving and jamming antenna selection to improve the secondary data transmission and primary secrecy performance respectively. This describes an attractive scheme in practice: unlike that in most existing approaches, the secrecy performance improvement in the CR network is no longer at the price of the data transmission loss. The outage probabilities for both the data transmission and physical layer secrecy are analyzed. Numerical simulations are also included to verify the performance of the proposed scheme.