Hydrocarbons, carbon monoxide, and other polluting emissions produced by diesel engines are usually much lower than those by gasoline engines. However, higher combustion temperature in diesel engines cause substantially larger percentage of nitrogen oxides (NOx) emissions. Selective catalytic reduction (SCR) is a well proven technology for reducing NOx emissions from automotive sources and in particular, heavy-duty diesel engines. In this paper, we develop a quasi linear parameter varying (qLPV) model to capture the nonlinearities in the dynamics of the ammonia SCR system with varying catalyst surface temperature. To effectively enable the use of LMI-based control design methods, the number of LPV parameters in the qLPV model is then reduced by using the principal component analysis (PCA) technique. An LPV feedback/feedforward controller is designed for the qLPV model with reduced number of scheduling parameters. The designed full-order controller is further simplified to a first-order transfer function with parameter-varying gain and pole. Finally, simulation results illustrate the high conversion efficiency with minimum ammonia slip of the closed-loop SCR system using the parameter-varying control law.