The urea-selective catalytic reduction (SCR) system is one of the effective after-treatment emission reduction methods for diesel engines that comply with the emission standards. This paper presents the development of a linear parameter-varying (LPV) model for the urea-SCR system from the identified linear models. To reduce the NO$_{X}$ emissions from diesel engines, a LPV model-based supertwisting sliding mode controller with lemniscate sliding surface is designed. The closed-loop performance of the designed controller is evaluated through simulations for step change in input and disturbance in output. The controller performance is compared against the multimodel PI controller and LPV model-based supertwisting sliding mode controller with linear sliding surface. The use of smooth and robust lemniscate sliding surface provides faster response as compared to the other two controllers. The control algorithms are compared using the performance indices and the proposed control scheme has the least settling time and rise time.