The vehicle braking system is one of the crucial issues in vehicle dynamics and automotive safety control. This research focuses on the implementation of a control scheme for allocation of the brake force for Through-the-Road (TtR) four-wheel-drive (4WD) Hybrid Electric Vehicle (HEV) to investigate the vehicle yaw stability control. The development of the mathematical models of the vehicle dynamic that comprised of rigid body dynamics, tire dynamics, longitudinal force and lateral force from the literature review are one of the most crucial steps to make sure the result obtained is closed as possible to the actual system. Robust controller is designed to control the vehicle yaw stability based on the electronic brake force distribution (EBD) braking system. By applying the robust control scheme, the vehicle yaw stability can be enhanced against the external disturbances. The performance of the proposed controller is compared based on the transient response's specifications to the reference signal response for the effectiveness analysis through simulation in the MATLAB/SIMULINK environment.