The　aim　of　this　paper　is　to　propose　a　new　measure　approach　of　ambiguous　risk　aversion　under　some　capacity　mu　(a　non-additive　measure),　in　particular,　under　the　distorted　probability.　Firstly,　by　using　the　Choquet　integral　with　respect　to　the　capacity　mu,　we　introduce　the　concept　of　ambiguous　risk　premium　rho(u)(X)　of　a　risk　asset　X　for　risk　aversive　individuals　whose　utility　function　is　u,　and　we　investigate　some　properties　of　the　ambiguous　risk　premium　under　some　assumptions.　Then　to　illustrate　our　theoretical　results,　we　give　an　example　and　empirical　results.