This study deals with the problem of green supplier selection for the electronics industry in Taiwan. After defining a problem-solving procedure, we use an analytic network process (ANP) model with benefits, opportunities, costs, and risks (BOCR) merits to assess all factors for ranking suppliers. This study then illustrates a real-world case of supplier selection for the adapter of one type of notebook PC. We also set up a radar chart to show the priorities of the factors under the four merits so that managerial implications can be drawn. Firms in the past mostly relied on tangible criteria for making purchasing decision instead of considering the uncertain opportunities and risks in the evaluating process. The ANP model with BOCR merits can incorporate the uncertainties into the model. First, we compile 12 general criteria and 6 green criteria on supplier selection. Second, we take on the content validity ratio and factor analysis for acquiring elements and clusters under the BOCR aspects and then apply the ANP approach to process the independence and feedback among elements and clusters. Third, we execute a sensitive analysis. Lastly, we present the priorities of all factors under different merits. The model simultaneously considers the general criteria and green criteria in order to reward the environmental efforts of the suppliers. The results show that valued clusters are slightly different from the aspects of BOCR, i.e., “production adaptability”, “promise to customer”, “price” and “product reliability” are the major concerns, whereas green criteria are less valued. In addition, the ANP with BOCR can describe the criteria and factors in details and also consider the effects of uncertainties for a suitable decision. In the final part, we draw up suggestions for the stakeholders in the hope that they put forth more efforts on environmental protection in the future.