We investigate the physical-layer security performance for a wireless-powered relaying mixed free-space optical-radio frequency (FSO-RF) system. In this system, a source transmits optical information to a relay (R), which decodes the received signal with a decode-and-forward protocol, converts it into an RF signal, and forwards it to a destination in the presence of an eavesdropper. Furthermore, we also assume that R has no extra power supply, and it only relies on harvesting energy from a power beacon to forward the information. Assuming that the FSO and all of the RF channels experience gamma-gamma and Rayleigh fading, the closed-form analytical expressions for secrecy outage probability and the probability of strictly positive secrecy capacity are derived. In addition, the effects of atmospheric turbulence, pointing errors, and detection techniques on the system performance are analyzed. Finally, we perform Monte Carlo simulations to verify the accuracy of the derived expressions.