In this paper a Godunov-type finite volume method is used for the solution of bedload sediment transport dynamics. The utilised equations for this modelling comprise the shallow water equations used for the hydrodynamic phase and also the Exner equation applied for the morphodynamic variations. These set of equations are then solved using a weakly-coupled scheme based on an augmented Riemann solver. In this approach the morphodynamic equation is first solved and the updated bedload changes with the same Riemann structure are used as a source term within the shallow water equations. The proposed numerical model is first used for the simulation of the parabolic sediment layer and the obtained numerical results are validated with the exact solution. Then, a bedload hump propagation with an initial subcritical condition which is able to create both mild and strong sediment and free-surface interactions is considered and the computed results are compared with the reference solution. These numerical results indicate that the defined weakly coupled method developed based on an augmented Riemann technique is able to be used for modelling bedload sediment transport for all flow regimes and exhibits a very good agreement with analytical or reference solutions for the given test cases.