It is important to have a precise model for the clutch damper in order to simulate the entire powertrain of a vehicle and predict the responses of the system. In this research, we developed a new model in which the spring used in the clutch damper is divided into a finite number of elements. The model takes many unique properties of arc-shaped springs into consideration and is anticipated to be more precise than conventional simple models. With the model, two meaningful results were presented which can be utilized afterwards. One is a simulation concerning the peak torque transmitted via the clutch damper. The other is a simulation that shows the hysteretic characteristics of the clutch damper.