In this article, we study the physical-layer security performance of the mixed millimeter-wave (mm-wave) radio frequency (RF) assisted free-space optical (FSO) system as a future candidate transmission technology. The Rician and the Gamma-Gamma fading are investigated for the mm-wave RF and the FSO channels, respectively. More precisely, to analyze the secrecy performance of our considered system, we derive exact closed-form expressions for the average secrecy capacity and lower bound of the secrecy outage probability. Our considered system model involves the fixed-gain and the variable-gain relaying protocols, mm-wave characteristics and pointing errors in the RF and the FSO links and finally the heterodyne detection and the intensity modulation with direct detection techniques. Monte Carlo simulation results are provided to verify our analytical results and also to investigate the effects of mentioned parameters and techniques in the security performance of the proposed mixed system.