In this paper, we investigate a multiple users cooperative overlay cognitive radio non-orthogonal multiple access (CR-NOMA) network in the presence of imperfect successive interference cancellation (SIC) and imperfect channel state information (CSI). In the context of cellular network, cell-center cognitive secondary users act as relays to assist transmission from the primary user (PU) transmitter to the cell-edge PU receiver via NOMA. According to the received signals between the primary transmitter and multiple cognitive secondary center users, the best cell-center cognitive SU with the maximum signal to noise ratio (SNR) is selected to transmit the PU’s signals and its own signal to cell-edge users through NOMA principle. Then, the PU cell-edge user combine the signals received from direct transmission in the first phase and relay transmission from the best cell-center cognitive SU in the second phase by selection combining (SC). To measure the performance of the system quantitatively, we derive the end-to-end outage probability and capacity for the primary and secondary networks by taking the imperfect SIC and CSI into consideration. Finally, the performance analysis is validated by the simulations, and show that serious interference caused by imperfect SIC and (or) imperfect CSI reduce the system performance.