One-dimensional numerical models using finite difference methods for unsteady sediment transport on alluvial river channel are developed. The Preissmann implicit scheme and the Lax-Wendroff two-step explicit scheme with the Method of Characteristics for water motion and a forward time centered space explicit scheme for sediment motion are developed to simulate the sediment transport rate and the variation of channel bed level. The program correctness of each model is successfully verified using volume conservation tests. The sensitivity studies show that higher peak stage level, steeper channel slope and longer flooding duration produce more channel bed erosion. and median grain size, $D_{50}=0.4mm$ give maximum volume loss in this study. Finally, the numerical models are found to produce reasonable results from the various sensitivity tests which reveal that the numerical models have properly responded to the changes of each model parameter.