A barrier discharge ignition apparatus has a tip end exposed to a combustion chamber of an internal combustion engine and, when subjected to a high-frequency high-voltage AC burst, generates streamer discharges for igniting a fuel/air mixture in the combustion chamber. A central electrode of the apparatus, covered by a dielectric layer and coaxially enclosed in a ground electrode, extends into the combustion chamber to a greater distance than the ground electrode. An electrode portion close to the tip end of the inner periphery of the ground electrode protrudes towards the dielectric layer, for creating a localized high-density electric field. The streamer discharges thereby enter both the to combustion chamber and also a discharge chamber of the ignition apparatus.