Abstract: This paper studied secure transmission in cooperative non-orthogonal multiple access (NOMA) networks, where one legitimate user with high-level security requirement (LU1) is overhead by multiple non-colluding eavesdroppers (Eves), and another normal user (LU2) is served by the source (Alice) simultaneously. Aiming to improve the secrecy performance, a cooperative jammer (Charlie) is employed to confound the Eves. In this more practical communication scenario, take both secrecy outage restriction of LU1 and the desired quality of service (QoS) demand of LU2 into consideration, the paper propose an adaptive power allocation strategy for maximizing secrecy rate under imperfect channel state information (CSI). Numerical results are provided to verify the effectiveness of the proposed scheme and show that the system security would be seriously degenerated with channel uncertainty.