Satellite communication systems serve as an indispensable component of wireless heterogeneous networks in 5G era for providing various critical civil and military applications. However, due to the broadcast nature and full accessibility of wireless medium, serious security threats exist from such systems. As an effort to address this issue, this paper, for the first time, investigates the secure communication in a non-geostationary orbit (NGSO) satellite system from a physical layer security perspective. Specifically, we focus on the downlink of an NGSO satellite which provides services to a fixed earth station and is wiretapped by a fixed eavesdropper. We first apply three types of orbiting models to characterize the movement state of the satellite. Based on the orbiting models, we then provide theoretical analysis for the secure communication performance of such a system. The expressions of two fundamental performance metrics, secrecy capacity and secrecy outage probability, are derived in a closed form for any system time. Finally, we conduct extensive simulations to validate our theoretical performance analysis and illustrate the security performance in a practical NGSO satellite communication system.