Disclosed are a cooling device and cooling method of an electrode for a large-power electric thruster. The cooling device comprises a refrigeration portion, a medium circulation portion and a controlportion. The control portion is used for adjusting and controlling the refrigeration portion according to the difference between a sensed temperature and a set temperature. The medium circulation portion is used for cooling the electrode. An existing large-power electric thruster lacks active cooling protection measures for the electrode in the working process. According to the cooling device of the electrode, a space inertia cooling mode is changed, and the cooling device is installed in combination with the large-power electric thruster. Through an active cooling mode with circulation of low-temperature refrigerants, the problem of fusing caused by too high working temperature of the original electrode is solved, the working temperature of the electrode of the large-power electric thruster is effectively lowered, the service life of the electrode is effectively prolonged, the service life of the electric thruster is indirectly prolonged, and the use cost of the electric thruster is lowered.