With the consistent development of the 3D application technique, visuals are available at more realistic quality and are utilized in many applications like game. In particular, interacting with 3D objects in virtual environments, 3D graphics have led to a substantial development in the augmented reality. This study proposes a 3D user interface to control objects in 3D space through virtual two-view method using only one camera. To do so, homography matrix including transformation information between arbitrary two positions of camera is calculated and 3D coordinates are reconstructed by employing the 2D hand coordinates derived from the single camera, homography matrix and projection matrix of camera. This method will result in more accurate and quick 3D information. This approach may be advantageous with respect to the reduced amount of calculation needed for using one camera rather than two and may be effective at the same time for real-time processes while it is economically efficient.