Disclosed are a driving apparatus of a passive matrix type electronic ink display device capable of driving the electronic ink display device precisely, improving a contrast of data displayed in the electronic ink display device, and simplifying a manufacturing process according to a simple construction of the electronic ink display device, and a method therefor. For this purpose, the method for driving the electronic ink display device comprises the steps of: applying a data voltage to at least one data line among a plurality of data lines; and applying a scan voltage only to one scan line selected among a plurality of scan lines while the data voltage is applied, and then floating the remaining scan lines other than the selected scan line.