Selecting the right contractor in construction industry is an important problem for an organization while the competition in global markets increases. Evaluating contractors' performance is a multiple attribute decision making process consisting of vagueness and imprecision. It is based on a set of hardly exact measurable attributes: capability and skills, occupational health and safety, technical capacity, managerial capability, bid amount, past performance and experience, financial soundness. The goals and interests of the stakeholders should be taken into consideration when selecting the attributes and their importance for the evaluation of contractors. In this context, the paper presents a novel method based on multiple attribute Weighted Aggregated Sum Product Assessment with the grey attributes scores -WASPAS-G method. The proposed method was applied in a case study of evaluation and selection of a right construction contractor, which has to be the most appropriate to stakeholders. The proposed technique, due to its capabilities of handling imprecise information because of applied grey relations and capabilities of providing decisions of enhanced accuracy when aggregating two methods, could also be used to sustain the ranking of development strategies, selecting the most effective investment or management decisions.