In an electroluminescence display apparatus and a driving method of an electroluminescence display apparatus, the electroluminescence display apparatus includes a pixel connected to a data line and a reference voltage line, the pixel including a driving element configured to generate a driving current based on a sensing data voltage supplied through the data line and a reference voltage supplied through the reference voltage line, and a level of the driving current being proportional to a level of the sensing data voltage, a comparison and tracking circuit configured to previously determine a target current range between a reference low current and a reference high current and change current tracking data for adjusting a level of the sensing data voltage until the driving current input through the reference voltage line is within the target current range, and a digital-to-analog converter configured to adjust a level of the sensing data voltage so as to be proportional to a size of the current tracking data and supply the level-adjusted sensing data voltage to the data line.