This paper considers the class of discrete-time nonlinear Markovian jump systems. The stochastic stability and stabilization problems are tackled. A model-based fuzzy stabilization design utilizing the concept of the so-called parallel distributed compensation (PDC) is employed to stochastically stabilize the class of systems under consideration. LMI-based sufficient conditions are developed to synthesize the state feedback controller that stochastically stabilizes the fuzzy stochastic system. Two examples are worked out to show the validness of the theoretical results.