Full-duplex non-orthogonal multiple access wireless networks with energy harvesting have the potential to improve spectral efficiency and save energy. However, wireless signals are susceptible to eavesdropping by other devices within their coverage area. This paper studies the security performance of a full-duplex non-orthogonal multiple access wireless network with energy harvesting (FDNOMAWNwEH) over Nakagami-m fading channels. Results show that the total throughput increases as the power of the primary transmitter increases. Similarly, the total throughput also increases as the expected security level or the energy harvester efficiency increases. In addition, there exists a value of the NOMA power division factor that maximizes the total throughput. Furthermore, the results show that the total throughput decreases as the fading severity parameter increases.