Estimating the human hand posture is important for a variety of applications, such as human-computer interface, virtual reality and computer graphic animation. However, posture recognition is not yet advanced enough to provide a flexible and reliable performance for these applications.The purpose of this study is to find a closed-form solution for 3D hand posture estimation using a 2D monocular image. In this paper, we propose a method to estimate the hand model parameters from detected 2D positions of finger tips and other main points. Using the hand model with 27 degrees of freedom (DOF) and the constraints among them, a new algorithm to estimate the finger posture by solving the inverse kinematics of the finger joints is presented. Experimental results confirm that our method gives the correct hand posture.