We analyze a secure dual-hop mixed radio frequency-free space optical (RF-FSO) downlink simultaneous wireless information and power transfer system. The FSO link and all RF links experience Gamma-Gamma, independent, and identical Nakagami-m fading, respectively. We analyze the effects of atmospheric turbulence, pointing error, detection technology, path loss, and energy harvesting on secrecy performance. Signalto-noise ratios at both the legitimate and illegitimate receivers are not independent since they are both simultaneously influenced by the FSO link. We derive the closed-form expression of the secrecy outage probability (SOP) as well as the asymptotic result for SOP when signal-to-noise ratios at relay and legitimate destinations tend to infinity. Monte-Carlo simulations are performed to verify the accuracy of our analysis. The results show that the secrecy diversity order (SDO) depends on the fading parameter of the relay-destination link and the number of the destination's antennas. In addition, the SDO also depends on the fading parameters, the pointing error parameter, and the detection type of the FSO link.