The run-ups of tsunamis and gravity water waves may induce considerable bed change in coastal areas. A numerical approximation for modeling bed load and suspended sediment routing is proposed in this study. As the time response of sediment movement is usually smaller than that of tides, the conventional method of morphological evolution that is used in river flow modeling can also be applied to sediment transport by tidal or coastal currents. Therefore, we adopt a coupled approach to solve the nonlinear shallow-water and sediment transport equations to approximate sediment transport and bed deformation. A  Godunov-type finite volume technique is used to solve the system of hyperbolic equations. The interface fluxes carrying the flow information are computed by an approximate Riemann solver technique 0f Harten-Lax-van Leer-Contact (HLLC). A TVD Runge-Kutta method and high-order reconstruction technique with limited gradient confirm second-order temporal and spatial accuracy, respectively. The proposed scheme has the ability to handle shocks arising in the solution due to bed discontinuities and abrupt changes in flow. Lastly, the numerical scheme is applied to some benchmark test cases to evaluate its adaptability and results are compared with previous studies.