Non-orthogonal multiple access (NOMA) has been considered as a promising technology for the fifth generation (5G) mobile communication system owing to its higher spectrum efficiency over conventional orthogonal multiple access (OMA). In addition, energy harvesting (EH), which can significantly improve energy efficiency, has attracted lots of attention. In this paper, a downlink NOMA-based EH (NOMA-EH) multiple antenna decode-and-forward (DF) relaying network is investigated over Nakagami-m fading channels. Transmit antenna selection (TAS) and maximal-ratio combining (MRC) are adopted at the source and users, respectively. The exact closed-form expression in terms of outage probability is derived. As a comparison, we also obtain the exact outage expression of the OMA-based EH (OMA-EH) system. Furthermore, the system throughput of NOMA-EH is studied as well as that of OMA-EH. Finally, the accuracy of the theoretical analysis and the advantage of NOMA-EH are validated by simulation results.