This paper proposes a 3D pointing interface that is designed for the efficient application of a hand mouse. The proposed method uses depth images to secure high-quality results even in response to changes in lighting and environmental conditions and uses the normal vector of the palm of the hand to perform 3D pointing. First, the hand region is detected and tracked using the existing conventional method; based on the information thus obtained, the region of the palm is predicted and the region of interest is obtained. Once the region of interest has been identified, this region is approximated by the plane equation and the normal vector is extracted. Next, to ensure stable control, interpolation is performed using the extracted normal vector and the intersection point is detected. For stability and efficiency, the dynamic weight using the sigmoid function is applied to the above detected intersection point, and finally, this is converted into the 2D coordinate system. This paper explains the methods of detecting the region of interest and the direction vector and proposes a method of interpolating and applying the dynamic weight in order to stabilize control. Lastly, qualitative and quantitative analyses are performed on the proposed 3D pointing method to verify its ability to deliver stable control.