A morphodynamic model for weakly dispersive wave and shallow flows in horizontal two-dimensional (H2D) space is proposed. The horizontal density variation and the bottom evolution are incorporated into a fully nonlinear Boussinesq equation including vorticity effects. By coupling the flow equation with the depth-integrated sediment transport equation, morphodynamic simulation is made possible. A fourth-order finite volume method with an approximate Riemann solver is used to solve the governing equations. For the hydrodynamic test under strong wave–current interaction environment, the accuracy of the computed velocity and water surface was verified. For the three typical morphological benchmark tests, such as tsunami, regular wave and dam break flow, good agreement was obtained when proper parameters were provided. Therefore, the proposed morphodynamic model can be a useful tool for a wide range of shallow and wavy flows under dispersive and nonhydrostatic environments associated with wave, current, and sediment interaction.