This paper shows the modelling and implementation of an adaptive cruise control (ACC) system for intelligent vehicles using fuzzy logic control approach. Initially, MATLAB Simulink is utilized to design an advanced vehicle model that takes into account most of the vehicle parameters using Simscape Driveline toolkit. Then, the fuzzy logic toolbox in MATLAB Simulink is introduced for designing and simulation of the fuzzy logic system. The proposed ACC algorithm functions in two different modes, the distance and velocity modes, based on the speed of the moving vehicle and the vehicle ahead. In distance control mode, the vehicle measures the actual distance to the vehicle ahead and compares it to the safe distance. If the measured distance is larger than the safe distance, the setpoint will be the safe distance and the system will work on maintaining the actual distance equal or greater than the safe distance. However, in speed control mode, the controller will operate according to the set speed adjusted by the driver given that the safe distance condition is met. This gives the vehicle the ability to make decisions relaying on both the set speed by the driver and the actual distance to the upfront objects. It is worth to mention that only a single controller is employed for both modes. According to MATLAB simulations, it is proven that the designed ACC algorithm using fuzzy logic controller is capable of retaining the vehicle in desired constraints as well as achieving satisfactory results owing to the simplicity of the proposed approach. The findings further demonstrate that the system have actually no overshoot with absolutely null steady state error while responding to the given speed with quite swift rising and settling times. However, there happen to be some rapid fluctuations in the throttle and brake values especially when the actual distance suddenly drops below the desired safe distance which may cause some driving inconvenience to the passengers.