This paper presents a one-dimensional numerical model for predicting sediment transport and bed evolution in natural rivers that have floodplains. The sediment transport in floodplains is generally different from that in the main channel. Even when erosion occurs in the main channel,the floodplain usually experiences deposition. To predict the erosion and deposition in the same cross section,the river is divided into three subchannels in the transversal direction: the main channel and the left and right floodplains. The non-equilibrium sediment transport equation is modified to account for the sediment exchanges between the subchannels. The numerical model has been applied to the stretch of the Rio Grande from San Acacia Diversion Dam to Elephant Butte Reservoir. Based on a comparison with field data,the bed profile and cumulative deposition are estimated satisfactorily by the numerical model.