The　Cloud　Distribution＇s　kurtosis　statistic　and　its　application　are　considered　to　analyze　and　improve　cloud　model　based　evolution　strategy　(CMES)　from　the　angle　of　the　classical　evolution　strategy.　By　adjusting　the　kurtosis,　the　Cloud　Distribution　with　a　fixed　standard　deviation　changes　the　shape　of　noise,　which　makes　the　mutation　more　effective.　The　formula　of　the　cloud　distribution＇s　kurtosis　is　derived,　which　enables　the　transformation　between　the　entropy-hyper　entropy　space　and　the　standard　deviation-kurtosis　space.　The　influences　of　the　kurtosis　and　the　kurtosis　ratio　on　the　cloud　distribution　noises　are　compared　to　prove　that　the　kurtosis　is　more　suitable　for　self-adaptive.　A　kurtosis　driven　CMES,　whose　parameter　evolution　combines　a　1/5　rule　based　standard　deviation　evolution　and　a　self-adaptive　kurtosis　evolution,　is　presented.　The　experimental　results　of　8　test　functions　show　that　a　high　kurtosis　benefits　global　optimization,　a　low　kurtosis　is　in　favor　of　local　optimization,　and　the　self-adaptive　adjustment　of　the　kurtosis　can　integrate　the　benefits　from　both.