Abstract: Leading cruise control (LCC) in mixed traffic has received wide attention as it can strengthen the capability of connected and automated vehicles in reducing traffic instability and smoothing mixed traffic. However, existing predictive LCC cannot directly address head-to-tail string stability (HSS) since velocity fluctuation of human-driven vehicles behind cannot be handled by constraint design in MPC framework. To address this challenge, this paper proposes a control matching MPC approach for LCC in mixed traffic. A head-to-tail string stable feedback controller based on the inverse optimal velocity model is designed to guarantee HSS under bilateral topologies. Then, an MPC controller is proposed and the weighting matrices in the objective function are tuned to match the MPC controller with the head-to-tail string stable feedback controller. Straightforward analysis of HSS and physical/safety constraints satisfaction are neatly combined by the proposed control scheme. The feasibility and closed-loop stability of the MPC controller are analyzed. Finally, simulations verify the effectiveness of the proposed controller.