A plasma display apparatus, more particularly to a plasma display apparatus for applying a negative sustain waveform while being driven and a method of driving the same are provided. The plasma display apparatus includes a plasma display panel in which a plurality of electrodes including scan electrodes and sustain electrodes are formed, driving parts for driving the plurality of electrodes, and a driving pulse controlling part for controlling the driving parts so that a scan reference waveform of a voltage level no more than a ground voltage level and a negative scan waveform of a voltage level lower than the voltage level of the scan reference waveform and higher than the voltage level of the negative sustain waveform are applied to the scan electrodes in an address period and that a negative sustain waveform is alternately applied to the scan electrodes and the sustain electrodes in a sustain period.