In the 5G era, satellite communication has been widely applied in more scenarios. Orthogonal Frequency Division Multiplexing (OFDM) has been adopted to the 3GPP standard and is the primary sync encoding method for satellite communication. However, the OFDM-based system is extremely susceptible to carrier frequency offset (CFO), and Doppler shift make a major impact on the CFO. Therefore, the traditional methods of synchronization based on OFDM cannot meet the requirement of satellite communication with large frequency offset and delay. There are many studies focus on improving the methods of CFO estimation and compensation to adapt the technologies of synchronization based on OFDM to the satellite communication system. In this paper, ZC based and matrix-vector multiplication method, multi-symbol merging method and preamble and PSS symbols based and filter frequency locked loop-based method of synchronization of OFDM-based satellite communication will be introduced. The accuracy and complexity of these methods both meet the requirement of 5G satellite communication system. Future researchers may focus on reducing complexity and expanding application scenarios.