Non-orthogonal multiple access (NOMA) is an important technology for the forthcoming 5 G and beyond. However, its privacy often suffers from adversarial eavesdropping, especially for the users with higher transmit power. In this paper, we propose a jamming-aided secure transmission scheme for cooperative NOMA networks with a full-duplex (FD) relay. In this scheme, two pairs of users perform secure transmission with the help of a decode-forward (DF) relay, which forwards information and generates artificial jamming to counteract eavesdropping. The precoding vectors are designed to zero-force the artificial jamming at legal receivers. Then, the channel statistics are calculated, based on which the secrecy rates of legitimate signals are analyzed and the expressions of secrecy outage probability (SOP) are derived. Furthermore, three benchmark schemes are also presented with their performance analyzed to verify the advantage of the proposed scheme. Simulation results show the accuracy of our analysis, and demonstrate that the proposed scheme can effectively reduce the SOP and improve the effective secrecy throughput via artificial jamming and FD relaying.