In this work a Laguerre Orthonormal Basis Functions Based Model Predictive Control (MPC) approach is proposed for automotive Adaptive Cruise Control (ACC) application in order to reduce optimization problem complexity. Model of ACC system is constructed using ego vehicle and inter-vehicular dynamics. For inter-vehicular distance control Constant Time Gap Policy is derived and to achieve the similarity with real world driver, an empirical driver model is utilized. Both approaches are integrated into the problem formulation. To avoid the effects of unmeasured disturbances on vehicle following performance, integral action is added to the system. Classical MPC approach is reformulated by representing control signal as sum of Laguerre Basis functions. Distance tracking error and control signal change is constrained to take safety measure and to cope with the system limitations. Additionally, to prevent infeasibility, slack variable approach is utilized. Classical MPC and proposed Laguerre MPC controllers are compared in terms of distance tracking performance and problem complexity.