The invention relates to a closed type small-gap multi-electrode gas switch device. The device has a sealed structure and is filled with sulfur hexafluoride gas with high insulating property, the sizes of internal electrodes can be reduced greatly, and gaps among the electrodes can also be reduced greatly, so that the size of the whole device is reduced; the nominal voltage of the switch device can be adjusted by the device according to the magnitude of inflating air pressure, and the circumstance that different grinding apparatuses are manufactured for products which are similar and are manufactured repeatedly is avoided; and moreover, the spherical electrodes are used for the device and are connected to one another through conductive portions in insulating struts, discharging gaps are formed, electric fields of the device are distributed reasonably, uniform resistors are respectively arranged at two ends of each gap, triggering signals are applied to each gap through a pulse voltage generator and a coupling capacitor, and spherical gaps or internal air pressure do not need to be adjusted. The closed type small-gap multi-electrode gas switch device is easy to operate, high in synchronicity and wide in triggering range, is not affected by external conditions, and is multipurpose although the model of the device is single.