The present study proposes a finite element model for numerical simulations of vegetated open-channel flows. 2D Characteristic Dissipative-Galerkin (CDG) method is used to solve shallow water equations with vegetation drag terms numerically. This numerical method, which belongs to Streamline Upwind/Petrov-Galerkin (SU/PG) method, damps out numerical oscillations along the characteristic lines. In the numerical model, vegetation within the watercourse is simplified to rigid cylinders. The vegetation model accounts for the volume reduced by cylindrical arrays, which is very important when vegetation is densely-populated. The model is also capable of simulating the transition from emergent to submerged vegetation or vice versa. First, the proposed model is validated by comparing the simulated results with experimental data. It is found that the model properly simulates the rise in flow water level and the fall in flow mean velocity due to vegetation. Then, the model is applied to a short reach of the Han River, in Seoul, Korea. The landscaped floodplains of the reach are now being considered by the city officials as one of the most important items to enhance the aesthetic of the river environment. The numerical simulations yield very interesting results that densely-vegetated floodplain increases the mean velocity of the main channel by about 20 % and decreases the mean velocity of the floodplains at both sides by about maximum 80 % and 30-50%.