A driving circuit in an organic electroluminescent device includes a gate driver unit for sequentially outputting a control signal to select gate lines in a luminescent array unit and a current driver unit for supplying picture data to a data lines in the luminescent array unit corresponding to the gate lines selected by the gate driver unit and selectively driving organic electroluminescent devices of the selected line. The driving circuit includes a minimum gray level judgment unit for determining whether the picture data is of a predetermined minimum gray level; and a switching unit for receiving a control signal according to the determination made by the minimum gray level judgment unit and for selectively supplying a reference voltage or a reference current to the selectively driven organic electroluminescent devices.