In physics, human body is a very complex deformable object with many degrees of freedom. Only with 2D appearance features, there exist a lot of difficulties in subtle motion analysis and recognition, and it is even more difficult to understand the user purpose. Since the gesture is an important approach for communication, based on 3D model, 3D pose of upper-limbs is reconstructed in this paper. For practical application and error reduction, the minimal conditions for pose estimation are analyzed, under which an end-fixed articulate model and the corresponding equations are proposed for nodeing the upper-limb and estimating the 3D coordinates of each joints. Then, maximal number of the resolutions is analyzed and an approach is given to obtain these ones. At last, two principles on the result error and the pose correctness are utilized for verification.