Adaptive cruise control (ACC), as one of the advanced driver assistance systems (ADAS), has become increasingly popular in improving both driving safety and comfort. It automatically adjusts vehicle speed to maintain a safe distance from the vehicle in front of it. Since the objectives of ACC can be multi-dimensional, and often conflict with each other, it is a challenging task in its control design. The research presented in this paper takes ACC control design as a constrained optimization problem with multiple objectives. A hierarchical framework on ACC control is introduced, aimed to achieve optimal performance on driving safety and comfort, speed and/or distance tracking, and fuel economy whenever possible. Under the hierarchical framework, the upper layer is based on a model predictive control (MPC) method employed to deal with the multiple control objectives, while the lower layer is for actuator control for vehicle longitudinal dynamics. Actuator delay is combined with the vehicle longitudinal dynamics by augmenting the system dimension to convert it into a delay-free system. A quadratic cost function is developed to obtain the ideal control output by solving the optimal control problem. The driving safety is guaranteed by constraining the inter-vehicle distance within a safe range. The requirements of other objectives are considered by designing particular performance indexes. The low-level controller serves as the actuator control unit, which controls the powertrain and brake systems to ensure that the desired acceleration is tracked based on the inverse longitudinal dynamics model. Finally, the proposed ACC is simulated and evaluated under PanoSim®, a virtual experimental environment for development, testing and verification of ADAS and intelligent driving in general. Simulation results have demonstrated satisfactory performance with the proposed ACC system.