Non-orthogonal multiple access (NOMA) and cognitive radio (CR) are considered as key technologies to improve the spectrum utilization of current mobile communication networks. Meanwhile, backscatter communication (BC) is a potential new green communication technology for IoT. In this paper, we propose an underlay CR-NOMA backscatter communication system, where the secondary network shares the spectrum of the primary network and the transmit power of the secondary source (ST) is constrained by the interference threshold of the primary network. Therefore, the ST adaptively adjusts its own transmit power and keeps the instantaneous interference power at the primary receiver (V) below the interference threshold, so that the instantaneous signal-to-noise ratio of the secondary network is maximized. Meanwhile, in the secondary network, the backscatter device receives the signal from the ST and divides it into two parts, one for its own energy supply and the other for modulated reflection to the cognitive near user U1 and the cognitive far user U2. Under the interference threshold constraint, we derive the exact analytical expressions for the outage probability of U1 and U2 using perfect successive interference cancellation (SIC). Finally, the accuracy of the theoretical analysis is verified by Monte Carlo simulation.