"The aim of this talk is introduce an Implicit-Explicit (IMEX) strategy to compute the sediment evolution in the Exner model for sediment transport in Shallow Water system and improve both stability and efficiency. In this model there are several time scales. One associated with the temporal evolution of the sediment, generally very long with a much slower velocity; one related to the velocity of free-surface waves, generally very fast that implies an hard restriction in the time step; and one related to the velocity of the fluid with. Unfortunately, as known, an explicit method implies a strong stability restriction due to the velocity of the free-surface wave. This restriction involves in a very long computation time that could be reduced neglecting the free-surface waves behaviour and looking at the sediment evolution. The objective is to drastically improve the efficiency in the computation of the evolution of the sediment by treating water waves implicitly, thus allowing much larger time steps than the one allowed by standard CFL condition on explicit schemes."