The purpose of this paper is to prove a Jensen type inequality for Choquet integrals with respect to a non-additive measure which was introduced by Choquet [1] and Sugeno [20]; $$Phi((C);{int};fd{mu});{leq};(C);int;Phi(f)d{mu},$$ where f is Choquet integrable, ${Phi};:;[0,;infty); ightarrow;[0,;infty)$ is convex, $Phi(alpha);leq;alpha$ for all $alpha;{in};[0,;{infty})$ and ${mu}_f(alpha);{leq};{mu}_{Phi(f)}(alpha)$ for all ${alpha};{in};[0,;{infty})$. Furthermore, we give some examples assuring both satisfaction and dissatisfaction of Jensen type inequality for the Choquet integral.