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Satellite communication system is expected to play an important role in wireless networks because of its appealing contributions to ubiquitous coverage, content multicast and caching, reducing user expenditure, and so on. However, due to the inherent broadcasting nature and serious channel conditions, satellite communication system is highly vulnerable to eavesdropping attacks. As an initial step towards this end, this paper focuses on the physical layer security technique and explores the secrecy performance of a multibeam satellite system, where multiple legitimate users are served and each user is exposed to an eavesdropper located in the same beam. With perfect channel state information at the satellite and adopting the complete zero-forcing approach for signal processing, we first derive the optimal beamforming vectors to maximize the achievable secrecy rate. Based on this, we further calculate the secrecy outage probabilities of an individual user and the whole system, respectively. Finally, simulation and numerical results are provided to show the secrecy performance of the multibeam satellite system.