Secure transmission is essential for future non-orthogonal multiple access (NOMA) system. This paper investigates relay-antenna selection (RAS) to enhance physical-layer security (PLS) of cooperative NOMA system in the presence of an eavesdropper, where multiple antennas are deployed at the relays, the users, and the eavesdropper. In order to reduce expense on radio frequency (RF) chains, selection combining (SC) is employed at both the relays and the users, whilst the eavesdropper employs either maximal-ratio combining (MRC) or selection combining (SC) to process the received signals. Under the condition that the channel state information (CSI) of the eavesdropping channel is available or unavailable, two effective relay-antenna selection schemes are proposed. Additionally, the closed-form expressions of secrecy outage probability (SOP) are derived for the proposed relay-antenna selection schemes. In order to gain more deep insights on the derived results, the asymptotic performance of the derived SOP is analyzed. In simulations, it is demonstrated that the theoretical results match well with the simulation results and the SOP of the proposed schemes is less than that of the conventional orthogonal multiple access (OMA) scheme obviously.