In this study, cooperative regenerative braking control of front-wheel-drive hybrid electric vehicle is proposed to recover optimal braking energy while guaranteeing the vehicle lateral stability. In front-wheel-drive hybrid electric vehicle, excessive regenerative braking for recuperation of the maximum braking energy can cause under-steer problem. This is due to the fact that the resultant lateral force on front tire saturates and starts to decrease. Therefore, cost function with constraints is newly defined to determine optimum distribution of brake torques including the regenerative brake torque for improving the braking energy recovery as well as the vehicle lateral stability. This cost function includes trade-off relation of two objectives. The physical meaning of first objective of cost function is to maximize the regenerative brake torque for improving the fuel economy and that of second objective is to increase the mechanical-friction brake torques at rear wheels rather than regenerative brake torque at front wheels for preventing front tire saturation. And weighting factor in cost function is also proposed as a function of under-steer index representing current state of the vehicle lateral motion in order to generalize the constrained optimization problem including both normal and severe cornering situation. For example, as the vehicle approaches its handling limits, adaptation of weighting factor is possible to prioritize front tire saturation over increasing the recuperation of braking energy for driver safety and vehicle lateral stability. Finally, computer simulation of closed loop driver-vehicle system based on Carsim (TM) performed to verify the effectiveness of adaptation method in proposed controller and the vehicle performance of the proposed controller in comparison with the conventional controller for only considering the vehicle lateral stability. Simulation results indicate that the proposed controller improved the performance of braking energy recovery as well as guaranteed the vehicle lateral stability similar to the conventional controller.