The growing attention of the recycling of WEEE led to the making of critical studies on how to manage this process such as to determine one of the most appropriate outsourcing firms. In the recent years, the determination of the most suitable firm to be managed for the recycling of WEEE for private and public institutions is a critical decision that has high level importance in terms of environmental, economic, social and even technological. For this aim, we try to determine the best alternative outsourcing firm for management of WEEE process for Municipality of Eyup which is a district located in European side of Istanbul by using suggested MCDM methodology based on HFS. In this paper, a multi criteria decision making (MCDM) methodology based on hesitant fuzzy enveloped TOPSIS that gives experts extra flexibility in using linguistic terms to give their assessments has been proposed to determine the best outsourcing firm for Waste of Electrical and Electronic Equipment (WEEE). We have developed a mechanism based on hesitant fuzzy sets (HFS) for enabling decision makers to be easier in evaluation process of WEEE management.