This paper considers a stochastic model predictive control of linear parameter-varying (LPV) systems described by affine parameter dependent state-space representations with additive stochastic uncertainties and probabilistic state constraints. In computing the prediction dynamics for LPV systems, the scheduling signal is given a stochastic description during the prediction horizon, which aims to overcome the shortcomings of the existing approaches where the scheduling signal is assumed to be constant or allowed to vary in a convex set. The above representation leads to LPV system dynamics consisting of additive and multiplicative uncertain stochastic terms up to second order. The prediction dynamics are reposed in an augmented form, which facilitates the feasibility of probabilistic constraints and closed-loop stability in the presence of stochastic uncertainties. © 2017 American Automatic Control Council (AACC).