The paper proposes a multi-attribute decision making method based on extended grey relation analysis under interval neutrosophic environment. The interval neutrosophic set is an important decision making apparatus that can handle imprecise, indeterminate, inconsistence information. The rating of the alternatives with respect to certain attribute considered by the expert is characterized by linguistic variables that can be represented by interval neutrosophic sets. In the selection process, the attributes are identified from the experts’ opinion. The weight of each attribute is completely unknown and maximizing deviation method is employed in order to determine them. Then, an extended grey relational analysis technique is developed to find the ranking order of all alternatives. Finally, an illustrative numerical example for weaver selection in Khadi Institution is provided to show the effectiveness and applicability of the developed approach