The present invention relates to an electro-luminescence display and a driving method thereof wherein a thin film transistor is prevented from the deterioration, to thereby improve a picture quality. An electro-luminescence (EL) display, including: a plurality of drive voltage supply lines; N compensation voltage supply lines; EL cells at each crossing of a plurality of data lines and a plurality of gate lines in a matrix, wherein the EL cells emit light in response to currents applied from the drive voltage supply lines; driving thin film transistors (TFT) connected between the EL cells and compensation voltage supply lines that control the current applied to the EL cells; and a bias switch, connected between the N−1th compensation voltage supply line and a control terminal of the driving TFT connected to the Nth compensation voltage supply line that applies a bias voltage to the driving TFT when a scan pulse is supplied to the N−1th gate line.