Sustainable investment is a hot topic of portfolio selection. This study aims to examine sustainable portfolio selection for conservative investors using the ESG criteria. Thus, we propose a two-stage integrated approach based on two-player zero-sum games. In the first stage, we use a fuzzy multi-criteria decision making (MCDM) approach to calculate the sustainability scores of the stocks based on expert knowledge. In the second stage, we form and solve a linear optimization problem by only adding a sustainability constraint to Young’s minimax portfolio selection model. We illustrate the integrated approach using the weekly simple returns of eight stocks. We also compare our results with the results of Young’s minimax portfolio selection model. We find that sustainable investment does not necessarily lead to performance loss. Furthermore, it may increase performance in some cases. To the best of our knowledge, this is the first paper on sustainable portfolio selection that depends only on two-player zero-sum games, including the stage of finding sustainability scores.