This paper presented a deep reinforcement learning method named Double Deep Q-networks to design an end-to-end vision-based adaptive cruise control (ACC) system. A simulation environment of a highway scene was set up in Unity, which is a game engine that provided both physical models of vehicles and feature data for training and testing. Well-designed reward functions associated with the following distance and throttle/brake force were implemented in the reinforcement learning model for both internal combustion engine (ICE) vehicles and electric vehicles (EV) to perform adaptive cruise control. The gap statistics and total energy consumption are evaluated for different vehicle types to explore the relationship between reward functions and powertrain characteristics. Compared with the traditional radar-based ACC systems or human-in-the-loop simulation, the proposed vision-based ACC system can generate either a better gap regulated trajectory or a smoother speed trajectory depending on the preset reward function. The proposed system can be well adaptive to different speed trajectories of the preceding vehicle and operated in real-time.