This paper presents the numerical approximation of bedload sediment transport due to shallow layer flows. The hydrodynamical component is modelled by a 2D shallow water system and the morphodynamical component by a solid transport discharge formula that depends on the hydrodynamical variables. The coupled system can be written as a non-conservative hyperbolic system. To discretize it, first we consider a Non-Homogeneous Riemann Solver scheme as well as a variant based on the use of flux limiters. In order to develop second-order scheme, we use a MUSCL method incorporating slope limiters in the spatial approximation and a two-step Runge-Kutta method for time integration. The comparison between results based on the proposed scheme and analytical results shows good agreement..