We　revisit　the　persistence　and　stability　property　of　a　stage-structured　prey–predator　model　with　cannibalism　and　constant　attacking　rate.　By　using　the　differential　inequality　theory　and　Bendixson–Dulac　criterion,　we　show　that　if　the　system　without　cannibalism　is　permanent,　then　the　system　with　cannibalism　is　also　permanent.　By　developing　some　new　analysis　technique,　we　obtain　a　new　set　of　sufficient　conditions　which　ensure　the　global　asymptotic　stability　of　the　nonnegative　equilibrium,　which　means　that,　under　some　suitable　assumption,　prey　cannibalism　has　no　influence　on　the　stability　property　of　the　predator　free　equilibrium.　Our　results　essentially　improve　the　corresponding　results　of　Limin　Zhang　and　Chaofeng　Zhang.　©　2020,　The　Author(s).