A three-electrode-discharge surge arrester has two opposing discharging parts of a pair of line electrodes, defining a gap therebetween, and a ground electrode disposed between the two discharging parts and provided with a penetration hole in the center. Each of the two discharging parts has a substantially conical shape. In accordance with this substantially conical shape, each of inner surfaces of upper and lower parts of the penetration hole of the ground electrode is substantially funnel-shaped. Hence, oblique parallel gaps for a primary discharge are formed between the substantially funnel-shaped inner surfaces of the upper and lower parts of the penetration hole and the two substantially conical discharging parts. Also, parallel gaps for a secondary discharge are formed between peripheral parts of the ground electrode around the penetration hole and peripheral parts of the line electrodes. Each of the oblique parallel gaps is formed narrower than each of the parallel gaps.