Mechanical systems using tendon-driven actuators have been widely used for bionic robot arms because not only the tendon based actuating system enables the design of robot arm to be very efficient, but also the system is very similar to the mechanism of the human body’s operation. The tendon-driven actuator, however, has a drawback caused by the friction force of the sheath. Controlling the system without considering the friction force between the sheath and the tendon could result in a failure to achieve the desired dynamic behaviors. In this study, a mathematical model was introduced to determine the friction force that is changed according to the geometrical pathway of the tendon-sheath, and the model parameters for the friction model were estimated by analyzing the data obtained from dedicated tests designed for evaluating the friction forces. Based on the results, it is possible to appropriately predict the friction force by using the information on the pathway of the tendon.