A　decision　method　of　integrating　the　prospect　theory　with　TOPSIS　is　proposed　for　multi-attribute　decision-making,　where　the　attribute　weights　are　unknown　and　attribute　values　are　in　the　form　of　hesitant　fuzzy　number.　Considering　the　different　attitudes　of　decision　makers　toward　index　sets,　An　approach　to　determine　the　weights　of　attribute　by　the　entropy　method　based　on　the　hesitant　fuzzy　entropy　is　proposed.　The　prospect　value　function　of　the　hesitant　fuzzy　number　is　defined　by　introducing　the　psychological　risk　factors　of　decision　makers　into　hesitant　fuzzy　multi-attribute　decision-making,　and　the　hesitant　fuzzy　decision-making　matrix　is　converted　to　the　value　matrix　based　on　which　the　ratio　of　gains　to　losses　of　the　alternatives　is　calculated.　Finally,　TOPSIS　method　is　used　to　rank　all　the　alternatives　and　a　numerical　example　is　provided　to　illustrate　the　effectiveness　of　the　proposed　method.　©　2017,　Editorial　Office　of　Control　and　Decision.　All　right　reserved.