The present study used the hydrodynamic numerical model, with the Reynolds-averaged Navier–Stokes equations (RANS) as its governing equations, to analyze overflow characteristics such as the discharge coefficient of circular-crested weir and the flow velocity and pressure distribution of weir crest. The simulation results well reproduced the overflow characteristics of the overfall of circular-crested weir both qualitatively and quantitatively. As for the discharge coefficient, rational results were yielded by the discharge coefficient equation proposed by Hager(1985) in the H1/Rb< 0.58 and by the discharge coefficient equation proposed by Samani and Bagheri(2014) in the H1/Rb> 0.58, respectively. Because most existing discharge coefficient equations were developed by disregarding the effects of the approach velocity, when they are applied, it is necessary to evaluate the effects of the approach velocity on the overflow head beforehand.