In this paper, a linear parameter-varying (LPV) model of a solution copolymerization reactor is developed by taking into consideration the time-varying nature of the parameters in the process. The aim is to design a controller that can ensure the stability and the desired performance of the copolymerization reactor in a prescribed range of operation. The LPV model complexity in terms of the number of scheduling variables is reduced by means of the application of a parameter set mapping (PSM) method which has proven to be effective in reducing the conservatism in LPV model development. The reduced model which only depends on one scheduling variable allows to reduce the complexity of the LPV controller synthesis for the process. Simulation results using the nonlinear model of the copolymerization reactor are provided to illustrate the improvements brought by the LPV controller in terms of reducing the convergence time and the control effort in comparison with a previously developed model predictive controller for the copolymerization process.