Abstract: In this paper, the upper bounds of the Choquet integral under a distorted probability measure are studied. Firstly, a necessary and sufficient condition for a function to be p-power logarithmically convex is given. Secondly, the upper bounds of the Choquet integral under a distorted probability measure are investigated for monotone, continuously differentiable p-power logarithmically convex functions. Finally, without imposing monotonicity or differentiability conditions, upper bounds of the Choquet integral are given for general p-power logarithmically convex functions.