This paper presents an algorithm for estimating the 3-D position of objects from monocular gray images. This algorithm has an advantageous property that needs no point-to-point correspondences. There are four steps in the algorithm. At the first, the 3-D shapes of object before and after rotation motion are recovered from image brightnesses. Then, moments of various order of the shape of the object are computed. Two vectors that are transformed according to rotation matrix under 3 D rotation, are constructed for the shape of the object before and after the rotation motion, respectively. At the third step, the rotation matrix is estimated using these vectors with SVD (Singular Value Decomposition). At the last, the rotation axis and the rotation angles are computed from the rotation matrix.