A display apparatus includes a display panel, a display panel driver, a light source part, a light directing element and a barrier driver. The display panel displays a 3D image by dividing a single 3D image frame into plural sub frames including one corresponding to a first stereoscopic view for display during a first sub frame and a second corresponding to a second stereoscopic view for display during a second sub frame. The light source part provides selectively blockable backlighting. The light directing element is disposed between the display panel and the light source part so as to implement selective blocking. The light directing element includes a barrier part and a lens part disposed on the barrier part. The barrier part has a plurality of first electrodes and a plurality of second electrodes crossing the first electrodes.