This paper investigates a multiple users cooperative cognitive non‐orthogonal multiple access (NOMA) network with energy harvesting. Primary transmitter and secondary sources serving as energy‐constrained nodes harvest energy from the power beacon PBS. In primary network, primary transmitter sends signals towards primary receiver. In order to make full use of spectrum resources, the secondary network access the licensed spectrum of primary network with overlay mode, where the best secondary source with maximum transmission signal‐to‐noise ratio between primary transmitter and secondary sources act as relays to forward signal via NOMA principle. In this context, two cooperative transmission protocols, namely, traditional NOMA cooperative transmission and adaptive NOMA cooperative transmission are proposed. For NOMA cooperative transmission, relays use NOMA to forward the superimposed signal of primary signal and secondary signal without any constrain. However, for adaptive NOMA cooperative transmission, relays use NOMA by judging whether the transmission between primary transmitter and primary receiver is successful or not. Primary receiver merges signals received from two transmission slots by selection combining. Finally, exact and asymptotic outage probability of primary network and secondary network with two cooperative transmissions are derived and simulated. It is shown that outage performance is improved for the proposed adaptive NOMA cooperative transmission.