Owing to its rotational symmetry and imaging invariance, a sphere has unique advantages when used as a spherical target in binocular vision systems. However, the image of a sphere on an image surface is generally an ellipse, rather than a standard circle, and the center of the ellipse does not coincide with the center of the sphere, resulting in errors when the location of the sphere's center is determined. To calculate accurate image coordinates of the center of a sphere to improve positioning accuracy, imaging models of spheres in space are established and analyzed, and a high-precision positioning method for the image of a sphere's center is presented based on the pinhole imaging model and perspective imaging principle. Combined with the focal length of the camera, the image coordinates of a sphere's center can be calculated after distortion correction of the edge points. The influence of edge noise and incomplete edge on this method is simulated and analyzed herein. Finally, the experimental results show that the proposed method can significantly improve the positioning accuracy of an image of a sphere's center; therefore, the proposed method is suitable for the positioning of a spherical target in a binocular vision system and for other applications requiring the accurate positioning of the center of a sphere.