A display device and a method for driving the display device are disclosed. The display device comprises a black and white liquid crystal display panel, an organic light emitting display panel, and a control unit. The control unit is configured to control the organic light emitting display panel to emit light, at least divide a frame of display time into a first time period, a second time period, and a third time period, and to drive the first primary color sub-pixel to emit light only in the first time period, the second primary color sub-pixel to emit light only in the second time period, and the third primary color sub-pixel to emit light only in the third time period. According to embodiments of the present invention, there is no need to provide lenticular lenses or a slit grating to realize 3D display, thus reducing production cost.