This paper studies the impacts of antenna selection algorithms in decode-and-forward (DF) cooperative nonorthogonal multiple access (NOMA) networks, where the secure information from the relay can be overheard by an eavesdropper in the networks. In order to ensure the secure transmission, an optimal antenna selection algorithm is proposed to choose one best relay's antenna to assist the secure transmission. We study the impact of antenna selection on the system secure communication through deriving the analytical expression of the secrecy outage probability along with the asymptotic expression in the high regime of signal-tonoise ratio (SNR) and main-to-eavesdropper ratio (MER). From the analytical and asymptotic expressions, we find that the system secure performance is highly dependent on the system parameters such as the number of antennas at the relay, SNR, and MER. In particular, the secrecy diversity order of the system is equal to the antenna number, when the interference from the second user is limited.