In this paper, we propose a secure transmission scheme to protect the confidential messages in a mixed free space optical-radio frequency (FSO-RF) relay network against malicious eavesdroppers. In the proposed scheme, the physical-layer key generation, encryption method and physical-layer wiretap coding are exploited to protect the FSO and RF links. Specifically, the overall transmission is divided into two time slots. In the first time slot, the transmitter and relay of the FSO link utilize the channel reciprocity of the FSO link to generate key packets. In the second time slot, the confidential messages will be securely transmitted from the transmitter to the receiver assisted by the relay over two phases. In the first phase, the transmitter sends the confidential messages to the relay through the FSO link encrypted by the generated key packets. In the second phase, the relay will forward these confidential messages to the receiver through the RF link protected by the physical-layer wiretap coding. For the proposed scheme, the key generation rate can be obtained. In addition, we analyze the performance of the connection outage probability and the secrecy outage probability, and optimally design the target transmission rate and secrecy rate such that the average secrecy rate is maximized. Numerical results are presented to demonstrate the performance superiority of the proposed scheme in terms of the average secrecy rate.