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This paper presents a blockchain-based approach for securing spectrum sharing in multi-beam satellite systems. Satellite spectrum is a scarce resource that requires highly efficient management schemes for optimized sharing by network users. However, spectrum sharing is vulnerable to attacks by malicious protocol participants. In order to ensure efficient spectrum management in the face of dishonest satellite users or cyber attackers, it is important for spectrum sharing mechanism to provide transparency and traceability of the trading process so as to enable the system to detect, and hence eliminate, unauthorized access by malicious users. We address these requirements by proposing the use of blockchain which, apart from its ability to provide transparency and traceability, ensures an immutable means for keeping track of user trading reputation. Besides, in order to address the practical constraints of heterogeneous user nodes, we also propose the use of edge computing to support users with limited computing power. In this paper, we propose a blockchain-based spectrum trading framework and, based on which, a multibeam satellite spectrum sharing algorithm for interference pricing and heterogeneous spectrum demands is devised to improve the efficiency of satellite spectrum. By leveraging on the system characteristics of blockchain, a dynamic spectrum sharing mechanism with traceability, openness and transparency for whole trading process is presented. Numerical results are also provided to evaluate the system benefits and spectrum pricing of the proposed mechanism.