Green Information Technology - IT - refers to IT practices and products that seek to prevent pollution and sustain development. By implementing Green IT practices, organizations can reduce the amount of energy spent and develop efficient technology products. However, the decision by an organization to adopt green IT is based on several considerations. Thus, this article puts forward an approach to support the decision process of adopting Green IT practices by group decision. Given this objective, SWOT analysis is an essential tool for strategic decision-making. It also combines the use of a multicriteria method with integer programming to support this process. Finally, a hypothetical case is presented in order to illustrate the applicability of the model.