Provided are a user interface device and a control method thereof for supporting easy and accurate selection of overlapped objects. The user interface device is a device for providing a user interface applied to a three-dimensional (3D) virtual space in which a plurality of virtual objects is created, and includes a gaze sensor unit to sense a user's gaze, an interaction sensor unit to sense the user's body motion for interaction with the virtual object in the 3D virtual space, a display unit to display the 3D virtual space, and a control unit to, when the user's gaze overlaps at least two virtual objects, generate projection objects corresponding to the overlapped virtual objects, wherein when an interaction between the projection object and the user is sensed, the control unit processes the interaction as an interaction between the virtual object corresponding to the projection object and the user.