In this paper, we investigate the physical layer security for an asymmetric dual-hop radio frequency-free space optical (RF-FSO) communication system, in which a source transmits information to a multi-aperture destination (D) through a best relay under the wiretapping of a multi-aperture eavesdropper (E). The best relay is selected by a partial relay selection scheme in terms of maximum instantaneous channel gain for the RF link. Moreover, equal gain combining scheme is also used to process the multiple copies of receiving signal at D and E. Assuming all the RF channels are subject to independent and identical distributed (i.i.d.) Nakagami-m fading and all the FSO channels are modeled by i.i.d. Gamma-Gamma process, the secrecy performance in terms of secrecy outage probability and the probability of strictly positive secrecy capacity are studied, and the accuracy of the analytical results is verified by Monte-Carlo simulations.