As customers' orientation towards environmental products increases, manufacturers and other members of the supply chain are looking for ways to conduct their operations in an environmentally and cost-effective manner. To find a solution that compensates these requests, a game theoretical approach is developed for a two-stage green supply chain consisting of a supplier and a producer. A Stackelberg game model based on asymmetric information structure is developed to find the optimal lot sizes and raw material sales price for raw material supplier, and the product sales price and the environmental cost for the producer. The developed approach is illustrated on a real-world case study that deals with production and raw material procurement processes of a plastic plug and compared to a scenario in which no environmental expenditures exist. The effect of changes in the model has been observed by tuning some significant parameters with the experimental design approach.