QBMPC is a recently developed technique for combined quality and tracking control of batch processes where prediction-based real-time control and batch-wise integral control are conducted simultaneously. The most important advantage of QBMPC is that both quality and tracking variables converge to the optima dictated by the objective function despite model uncertainty and run-wise repeating disturbances. In this paper, with the purpose to enhance the quality control aspect, the QBMPC algorithm has been newly formulated based on a time-varying state space model. The new algorithm has been applied to a batch reactor model for methylmethacrylate (MMA) polymerization where the weight-average molecular weight and polydispersity index of the end product, and monomer conversion are considered important quality variables to control. Key steps for the controller design are described and the resulting control performance is demonstrated.