This paper proposes the concept of an interval neutrosophic hesitant fuzzy set (INHFS) and the operational relations of INHFSs. Then, we develop correlation coefficients of INHFSs and investigate the relation between the similarity measures and the correlation coefficients. Furthermore, a multiple attribute decision making method based on the correlation coefficients is established under interval neutrosophic hesitant fuzzy environment. Through the correlation coefficients between each alternative and the ideal alternative, we obtain the ranking order of all alternatives and the best one. Finally, an illustrative example of investment alternatives is given to demonstrate the application and effectiveness of the developed approach.