Abstract: A sealing element and a sealing method for sealing both ends of an anode-supported tubular solid oxide fuel cell. The sealing element utilizes a coupling tube having one end opened to an exterior and a second end with a perforation hole, in which the coupling tube is formed with an internal cavity having a shape corresponding to an external appearance of an end portion of a fuel cell. A flow tube having a hollow section axially extends outwards from the second end of the coupling tube while communicating with the perforation hole. The sealing method involves cleaning the sealing element and fuel cell, surrounding an outer peripheral surface of an electrolyte layer on the ends of the fuel cell with a metallic filler material, inserting the fuel cell in a connection tube of the sealing element, heating and melting the filler material, and solidifying the melted filler material.