A display device having a scope of accreditation in cooperation with a depth of a virtual object and a controlling method thereof are disclosed in this specification. The display device according to this specification outputs a three-dimensional (3D) image including virtual objects. And a scope of accreditation accrediting (or recognizing) that a virtual object has been selected is configured in the virtual object. At this point, an area of a scope of accreditation may be configured to be in cooperation with a depth of a virtual object along an increasing or decreasing direction of the depth of the virtual object, wherein the depth of the virtual object indicates a distance level between the virtual object and a user's perspective within the 3D image.