Grain-size distributions of bedload sediment are modelled by considering the time variation of sediment transport in a unidirectional turbulent flow. A frequency distribution of instantaneous bed shear stress is divided into a large number of shear stress ranges with mean values of tau oi . Each tau oi is capable of transporting a range of sediment sizes as bedload; the maximum size is just at its entrainment threshold, the minimum size is just too large to be suspended. Rates of bedload transport are calculated for each size range using a theoretical bedload function, and the proportion of time that these rates occur is obtained by integrating the frequency distribution between the boundaries of each shear stress range. The relative weights of sediment transported in particular size ranges, determined for all tau oi values, constitutes the grain-size distribution obtained from bedload sampling at a fixed point on the bed. Cumulative grain-size curves have been simulated using the model in order to demonstrate the effects of the various model parameters (e.g., mean bed shear stress, viscosity). All curves show a distinct "break" in slope, which represents the maximum grain size transportable in suspension when the shear stress attains its maximum fluctuating value. Examination of many natural bedload distributions shows close qualitative and quantitative agreement with the model, and reasons for discrepancies can be fully explained. Typical grain-size distributions of deposited sediments can be obtained by mixing of different flow-related bedload distributions in various proportions. Thus although deposited sediments may primarily result from bedload transport during a steady flood flow, flow unsteadiness also plays a part. The effects of some deposition directly from suspended load can also be surmised.