This paper presents a robust yaw moment controller design approach for improving vehicle handling and stability. With considering the parameter-varying property of tyre cornering stiffness in extreme handling situations, a linear parameter-varying (LPV) model in polytopic form is constructed to represent the nonlinear characteristics of tyres. A yaw moment controller is then designed for the LPV model which aims at optimising the tracking performance on both yaw rate and sideslip angle with respect to their targets. The conditions for designing such a controller are derived in terms of linear matrix inequalities (LMIs). Numerical simulations on a nonlinear vehicle model are performed to validate the effectiveness of the proposed approach. The results show that the designed controller can improve vehicle handling and stability regardless of varying road surface.