Dynamic wireless charging (DWC) of electric vehicles (EVs) can greatly alleviate "short driving range" concern, making it a highly feasible prospect for electrified transportation. To achieve maximum power transfer in DWC, it is essential that the primary coil (under the road) and secondary coil (below the EV) are fully aligned. Lateral misalignment (LTM) occurs when the coils fail to align properly. The energy losses caused by LTM can be compensated using conventional controllers, however, they cannot perform well in higher misalignment scenarios and exhibit overshooting, and steady-state error (SSE). In this paper, a model prediction-based approach is implemented to design a controller that nullifies the LTM effect and compensates for the reduced power transfer to the EV. This work presents a comparative study between the model predictive controller (MPC) and conventional Proportional-Integral (PI) controller in terms of performance and suitability. The MPC controller uses an optimization algorithm to select the optimal control action over the prediction horizon, minimizing SSE and reducing overshooting in the system, thereby performing exceptionally well across all degrees of LTMs. The effectiveness of the proposed MPC has been evaluated through simulations in MATLAB/Simulink and experimental tests. The proposed MPC demonstrates superior performance compared to the PI controller in both simulation and experimental evaluations.