Supply chain management is an emerging topic in the oil and gas industry. There is higher exposure of contractors to undesirable incidents and supplier selection is a multicriteria decision problem (MCDM). A fuzzy-TOPSIS method was employed in the evaluation of three suppliers regarding four HSE criteria. This method was applied in a case study of the oil and gas industry involving a contractor bidding process. Results reinforced that fuzzy-TOPSIS is a versatile and suitable method for supplier selection problems, with low computational complexity and promoting a better user experience. This method contributes to greater effectiveness and agility in the selection processes of suppliers regarding HSE management. The fuzzy-TOPSIS model is suitable for supplier selection problems and some of the benefits of applying this method are that it allows the attribution weights according to the level of importance of each criterion and considers the complexity, subjectivity, and uncertainty of the decision process. One has determined that it was essential to have a robust and consistent process for weighting the criteria and defining the most appropriate linguistic variables.