A luminescence driving apparatus, a display apparatus, and a driving method thereof are provided. The luminescence driving apparatus includes: a driving circuit which is connected to a light-emitting device and drives the light-emitting device according to a control pulse having a fluctuating amplitude; a controller which, if an internal current of the light-emitting device is less than or equal to a threshold value, selects a position from among a plurality of different positions of the driving circuit based on the amplitude of the control pulse, senses a voltage at the selected position and determines whether a short-circuit has occurred between the light-emitting device and the driving circuit using a level of the sensed voltage; and a protector which if it is determined that the short-circuit has occurred, performs a protection operation with respect to the light-emitting device.