The control of joint stiffness of a robot is extremely important to guarantee safe and dexterous motion, especially for the collaborative operation between a human and a robot. Some devices to vary the joint stiffness have been proposed for a tendon-manipulator so far. However, the previous devices have problems such as a complex structure, increase of friction, increase of inertia and so on. In order to overcome these problems, we proposed a belt-formed pulley to vary the joint stiffness. Inserting the belt-formed pulleys into routes of wires, the joint stiffness of a tendon-driven robot can be varied depending on internal force among wires. The system using belt-formed pulleys has many advantages such as a simple structure, low friction, lightness in weight and low cost. However, little is known about kinematic issues of the tendon-manipulator using belt-formed pulleys. In this paper, we propose a numerical solving method of forward kinematics (to obtain joint angles from wire length) using approximate models of a belt-formed pulley. First, we propose three approximate models of a belt-formed pulley, and investigate usefulness of each model. Secondly, we present the numerical solving method of forward kinematics for a 1-DOF manipulator. Lastly, the usefulness of the proposed method is demonstrated through experimental result.