This paper studies the physical layer security in cognitive relay network (CRN) with multiple antennas in the presence of multiple eavesdroppers. Under spectrum sharing scenario and orthogonal space-time block code (OSTBC) transmission, we derive both the exact and asymptotic expressions of secrecy outage probability over Rayleigh fading channels and give the reliability-security tradeoff analysis. The results which have been verified by Monte Carlo simulation show that the loss of the secrecy outage performance caused by an increase of eavesdroppers number can be totally overcome by multiple antenna diversity. It's illustrated that increasing the number of antennas can also improve both reliability and security of the system. Besides, the asymptotic analysis indicates the secrecy diversity order is only determined by number of antennas and is independent with number of eavesdroppers. The secrecy array gain is relevant with both number of antennas and eavesdroppers. In other words, the existence of eavesdroppers will degrade the secrecy outage performance but will not affect the diversity order of the system.