The embodiment of the invention provides a display device and a drive method thereof, relating to the technical field of display. The display device comprises a display panel, a position sensor, a liquid crystal lens and a controller, wherein the position sensor is used for detecting at least one observation position in an observation area; the liquid crystal lens is arranged on the light-out side of the display panel; and the controller is connected with the position sensor and the liquid crystal lens and used for determining a main observation position from the at least one observation position and adjusting the deflection direction of liquid crystal molecules in the liquid crystal lens so that the emergent light of the liquid crystal lens is gathered to the main observation position. According to the invention, the main observer can be actively identified, and the image display direction is adjusted so that the displayed image cannot be seen from other positions but can be seen at the position of the main observer.