This work presents a new finite volume Godunov-type model for predicting morphological changes under the rapidly varying flood conditions with wetting and drying. The model solves the coupled shallow water and Exner equations, with the interface fluxes evaluated by an Harten-Lax-van Leer-Contact (HLLC) approximate Riemann solver. Well-balanced solution is achieved using the surface gradient method and wetting and drying are handled by a non-negative reconstruction approach. The new model is validated against several theoretical benchmark tests and promising results are obtained.