This paper presents an efficient stochastic model predictive control (SMPC) framework for quasi-linear parameter varying (qLPV) systems. The framework applies to general nonlinear systems that are driven by stochastic additive disturbances and subject to chance constraints. The qLPV form is featured by a composition of a set of linear time-invariant (LTI) models with state-/control-dependent scheduling variables, which can be obtained by the spatial–temporal filtering-based system identification approach developed in our earlier work. The overall framework can then be transformed into a tube-based MPC optimization problem which can be efficiently handled by a series of quadratic programing (QP) problems. A case study on automotive engine control is presented as a pilot demonstration of the proposed qLPV–SMPC where we show its advantage over the zone-based MPC, much greater computational efficiency than nonlinear MPC (NMPC) and less conservativeness of the proposed method as compared to its robust MPC (RMPC) counterpart.