Clutch judder has serious impacts on the noise, vibration and harshness performance. In this article, a simplified dynamic model with nonlinear friction torque is developed to simulate clutch judder, and the stability and dynamic response of the clutch are analysed. The real part of the judder modal eigenvalue, the moment when the clutch enters the stick state and the fluctuation level of the driving part of the clutch are treated as the evaluation indices. An uncertain hybrid model with random and interval variables is used to describe the uncertainty of parameters and a hybrid perturbation vertex method is formulated to compute the uncertainty. Furthermore, parameters with high sensitivities are used as design variables and uncertainty-based optimization is conducted to reduce clutch judder. The optimization results strongly validate that the proposed method is very effective in improving the robustness of the clutch judder performance.