In an organic electroluminescence display device (30) comprising an organic EL element (26) having a structure wherein an organic luminescent medium (24) is sandwiched between a top electrode (20) and a bottom electrode (22), and a driving circuit (14) for driving the organic EL element (26), the organic luminescent medium (24) comprises a host compound and a triplet-related luminous compound and the driving circuit (14) applies a electric pulse voltage or pulse current having a frequency of 30 Hz or more and a duty ratio of 1/5 or less. In this way, it is possible to provide an organic EL display device which consumes a low electric power and has a long luminous life span, and a method for driving the same.