In this paper, the H∞ output feedback control problem for a class of stochastic discrete-time systems with randomly occurring convex-bounded uncertainties and channel fadings is investigated. A sequence of mutually independent random variables with known probabilistic distributions are utilized to describe the randomness that convex-bounded uncertainties appear in practical systems. The measurements with channel fadings are given by a stochastic Rice fading model which is regulated by a set of random variables with certain probability density functions. The purpose of this paper is to design an output feedback controller such that the closed-loop control system is asymptotically stable with a prescribed H∞ performance level. The less conservative results are obtained by employing the stochastic Lyapunov technique. Numerical examples are presented to illustrate effectiveness of the proposed approach.