The computation of temporal variation of clear-water scour is important for the design of bridge foundations. Previous studies implied that a very long flow duration is needed to achieve equilibrium scour at bridge abutments. However, the corresponding durations in the prototype conditions may yield considerably greater values than the time to peak of most of the design floods of small to medium sized catchment basins. Therefore, there is a need to estimate the temporal variation of scour depth. This study deals with development of a semi-empirical model for determining the time-dependent variation of clear-water scour depth at vertical-wall abutments. This approach applies the sediment continuity equation to a scour hole around a vertical-wall abutment. A sediment pickup function was used to formulate the rate of sediment transport from the scour hole. The results of the proposed model were compared with those of empirical models. The model agreed well with the test results.