The　aim　of　this　paper　is　to　propose　an　approach　of　measurement　of　the　uncertainty　aversion　under　the　distorted　probability.　The　main　notion　studied　in　this　paper　is　the　uncertainty　premium　associated　with　a　distortion　function　g　and　a　utility　function　u.　Under　some　assumptions,　we　investigate　the　properties　of　uncertainty　premium　in　term　of　the　utility　function　u,　some　indicators　under　distorted　probability　and　the　distortion　function　g.