This paper investigates the predictive control synthesis problem for constrained feedback control systems with both missing data and quantization. By introducing a missing data compensation strategy and an augmented Markov jump linear model with polytopic uncertainties, the effects of data loss and quantization on the system performance are considered simultaneously. A robust predictive control synthesis approach involving data missing and recovering probabilities is developed by minimizing an upper bound on the expected value of an infinite horizon quadratic performance objective at each sampling instant. Additional conditions to satisfy the input constraint in the presence of multiple missing data are also incorporated into the model predictive control (MPC) synthesis. Furthermore, both the recursive feasibility of the proposed MPC algorithm and the closed-loop mean-square stability are proved. Simulation results are given to illustrate the effectiveness of the proposed approach. (C) 2015 Elsevier Ltd. All rights reserved.