In this paper, we investigate the performance of the non-orthogonal multiple access (NOMA) system with incremental relaying, where the relay is employed with amplify-and-forward (AF) or decode-and-forward (DF) protocols. To characterize the outage behaviors of the incremental cooperative NOMA (ICN) system, new closed-form expressions of both exact and asymptotic outage probability for two users are derived. In addition, the performance of the conventional cooperative NOMA (CCN) system is analyzed as a benchmark for the the purpose of comparison. We confirm that the outage performance of the distant user is enhanced when ICN system is employed. Numerical results are presented to demonstrate that (1) the near user of the ICN system achieves better outage behavior than that of the CCN system in the low signal-to-noise ratio (SNR) region; (2) the outage performance of distant user for the DF-based ICN system is superior to that of the AF-based ICN system when the system works in cooperative NOMA transmission mode; and (3) in the low SNR, the throughput of the ICN system is higher than that of the CCN system. authors of [9] have researched the performance of a downlink single-cell NOMA network when assuming imperfect channel state information (CSI) and second-order statistics. Furthermore, the authors in [10] consider the scenario that each user only feedback one bit of its CSI to a base station (BS) and analyzed the outage performance. Apart from these researches, there are a lot of studies on improving the secrecy performance of multiple users [11,12], where the external and internal eavesdropping scenarios have been considered. Up to now, NOMA has been extended to cooperative communication systems [13, 14], as the higher diversity and extended coverage can be obtained in wireless networks. The authors have analyzed the outage performance of NOMA system with decode and forward (DF) relay employing full-duplex (FD) and half-duplex (HD) mode, where the near user was selected as a relay to deliver information and improve transmission reliability of distance users [15]. Inspired by this, simultaneous wireless information and