The invention discloses an IT-SOFC (Intermediate Temperature Solid Oxide Fuel Cell) stack alloy connecting body and a connecting method of a cell stack. Alloy specifications with two different components of an anode chamber connecting body and a cathode chamber connecting body are adopted, and the pertinence on corrosion resistance of the connecting bodies is higher due to a specification difference of the anode and cathode alloy connecting bodies, so that the service life of the solid oxide fuel cell stack is prolonged. The alloy connecting body designed by a sheet through groove is arranged between every two single cells, so that the machining forming cost of the alloy connecting bodies is lowered. The invention further provides a parallel electricity connection method of the connecting bodies in the cell stack. According to the IT-SOFC stack alloy connecting body and the connecting method, the service lives of the alloy connecting bodies in the cell stack are prolonged, and the manufacturing economy and the operation stability of the cell stack are improved.