Car-following is an important driving behaviour for intelligent vehicles and has a significant impact on traffic efficiency and traffic safety. Car-following models are widely developed to characterize the human-drivers car-following manoeuvre actions and adopted in traffic simulation and automated vehicle control system development. Car-following models need to be able to represent the drivers behaviour while following preceding vehicles. On the other hand, car-following controllers are an important component of intelligent vehicle systems, both for autonomous vehicles and connected vehicles. However, Adaptive Cruise Control (ACC) as well as Cooperative Adaptive Cruise Control (CACC) do not include human behaviour, which makes their car-following behaviour not human-like or natural for the on-board driver or passenger. To address this problem, in this study, the human-like Wiedemann car-following model is calibrated and verified with our driving simulator data. A human-like car-following nonlinear model predictive control (MPC) controller is developed based on the calibrated car-following model. Three different scenarios are tested to evaluate the performance of the proposed controller, with which the autonomous vehicle is able to have human-like and smooth trajectories at different phases and within different transition zones.