This paper investigates the physical layer security of non-orthogonal multiple access (NOMA) with decode-and-forward (DF) relays in underlay cognitive radio (CR) network. Secondary transmitter communicates with legitimate users via the aid of relays, while the eavesdroppers try to intercept the message. To safeguard legitimate communications against eavesdropping, the joint of artificial-noise (AN) and relay selection (RS) is applied. We derive the secrecy outage probability (SOP) and the secrecy throughput to evaluate the secrecy performance. In addition, the asymptotic floor of SOP is derived. Numerical results verify that cooperative NOMA in underlay CR (CRNOMA) significantly outperforms the conventional orthogonal multiple access (OMA) in underlay CR network (CROMA) in terms of the secrecy outage performance. Furthermore, the effect of some critical parameters on the secrecy performance has been studied.