This study intends to propose a non-oriented DEA based game cross-efficiency approach for supplier selection. With a discussion on the choice of DEA models and approaches that are most appropriate for supplier selection, we propose a game cross efficiency model based upon the non-oriented variable returns-to-scale RAM DEA by adapting the existing game cross efficiency model based upon the oriented constant returns-to-scale CCR DEA. We develop the RAM game cross efficiency model and a convergent iterative solution procedure to find the best game cross efficiency scores that constitute a Nash equilibrium. We illustrate the proposed model with two data sets of supplier selection, and demonstrate that significantly different results are obtained when compared with the existing approaches.