Although the cost-saving and good environmental impacts are the benefits that make Electric Vehicles (EVs) popular, these advantages are significantly influenced by the cost of battery replacement over the vehicle lifetime. After several charging and discharging cycles, the battery is subjected to energy and power degradation which affects the performance and efficiency of the vehicle. In addition to battery replacement cost, the electricity cost being paid by drivers is another key factor in selecting the EVs. An Energy Management System (EMS) with Model Predictive Control-based (MPC) algorithm is presented for a specific case of heavy-duty EV. Such EV draws its energy from the grid via catenary in addition to the on-board battery. Dynamic model of the vehicle will be defined by State Space Equations (SSE). The simulation results for MPC-based EMS of a Catenary-based Range-extended Electric Vehicle (CREV) is presented, the control aim is to manipulate the power flow from the grid in order to minimize the cost of purchased electricity from grid and improve the life time of the battery will be presented.