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