The outage performance of cooperative Non-Orthogonal Multiple Access(NOMA) network adapting Amplify and Forward(AF) is investigated. In the multi-user multi-relay cooperative NOMA network, in order to guarantee the Quality of Service(QoS) requirement of the signal with low latency in the mixed signal, a power allocation scheme is proposed, and then the detection constraint conditions are obtained. Furthermore, for the given relay, the set is built according to the detection constraint conditions, and the user relay pair which can maximize the rate of high QoS signal is selected as the best “user-relay” to transmit the message. The expression equation of the system’s outage probability for the proposed user-relay selective scheme is derived and the asymptotic expression is solved. Simulation results prove the correctness of the derived results, and show that the system’s outage probability decreases with the increasing of the number of the relays. Especially when the Signal-to-noise ratio tends to be infinite, the system’s diversity gain is depended on the number of the relay. In addition, the outage performance of the proposed scheme is better than that in other existing literatures.