This paper considers the application of non-orthogonal multiple access (NOMA) into cooperative cognitive radio (CR) networks with simultaneous wireless information and power transfer (SWIPT). For NOMA in cooperative CR networks with SWIPT, the cognitive relay harvests the transmission power from the secondary transmitter with power splitting scheme, while the fixed power allocation scheme is used for the NOMA protocol. The closed-form analytical expression of the overall outage probability for the proposed networks is derived, as well as its diversity order at high signal-to-noise ratio (SNR) region is investigated. Furthermore, compared to OMA in cooperative CR networks with SWIPT, the proposed scheme can always achieve the same diversity order, but lower overall outage performance. Compared with NOMA in cooperative CR networks using its own battery for transmission, the SWIPT NOMA in cooperative CR networks will lead to losing a little of the overall outage performance, but without losing the diversity order. INDEX TERMS Non-orthogonal multiple access, cognitive radio network, decode-and-forward, simultaneous wireless information and power transfer, outage probability, diversity gain.