Natural gas liquefaction process is an energy intensive process due to its cryogenic condition. Therefore, one of the major objectives for the design and the optimization is the minimizing total energy consumption. Another important objective is the minimizing cost of the energy supply system. This research focused on the cost based optimization. First, the energy minimization for the mixed and the pure refrigerant systems was performed by deterministic optimization model. Then, the cost minimization for energy supply to the process was performed by the driver selection model. The driver selection model was built as mixed integer linear programming (MILP). As the result, 15 to 17% of energy saving was checked for the refrigerant system. At that time, optimal driver set which is the minimum cost for the energy supply system was found.