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How to realize safety data sharing and promote the integration of multi-source data is one of the important technical challenges faced by academic and industrial circles. In recent years,federated learning has received widespread attention, which is a new technology to deal with this challenge. Federated learning has been applied in fields such as smart healthcare and smart city construction, but there is little research in the field of potential trajectory data mining. To solve this problem, this paper proposed a distributed and secure framework named federated spectral clustering( FSC), and applied it to the spectral clustering of ship AIS trajectory data. In the FSC framework, it used the encrypted sample alignment technology and a homomorphic encryption scheme as building blocks for the clustering algorithm, guaranteeing the security of the data in the process offederal training executed by multi-participants. To illustrate the effect of this algorithm, this paper conducted the experiments on both synthetic datasets and ships AIS trajectory datasets. The comparisons of experiments results with other similar clustering algorithms demonstrate that, besides its security advantage, this algorithm performs well in terms of clustering effect. The results indicate that the FSC can obtain the main route in the marine navigation area, which can provide specialized support for the intelligence of maritime supervision systems. [ABSTRACT FROM AUTHOR]