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Hesitant fuzzy sets (HFSs) proposed by Torra and Torra and Narukawa have been provedto be more practical in handling fuzziness. The feature of HFSs to assign membership degreesin the form of a set has made them very useful for solving multiple attribute decision making(MADM) problem. In this communication, we have introduced anew exponential hesitantfuzzy entropy based on well-known exponential entropy studied by Pal and Pal. The proposedentropy is then used for solving MADM problem. The attributes weights play an importantrole in solution of MADM problem. In this study, two methods are discussed to determineattributes weights. Finally, two numerical examples are given to illustrate the effectivenessand feasibility of proposed method.