This study analyzed the hydraulic characteristics of a venturi flume with a circular cone using a 3-D numerical model which uses RANS(Reynolds-Averaged Navier-Stokes Equation) as the governing equation. The venturi flume with the circular cone efficiently measures the discharge in the low-flow to high-flow range and offers the advantage of accurate discharge measurements in the case of a low flow. With no influence of the tail-water depth, the stage-discharge relationship and the flow behaviors were analyzed to verify the numerical simulation results. Additionally, this study reviewed the effect of the tail-water depth on the flow. The stage-discharge relationship resulting from a numerical simulation in the absence of an effect by the tail-water depth showed a maximum margin of error of 4 % in comparison to the result of a hydraulic experiment. The simulation results reproduced the overall flow behaviors observed in the hydraulic experiment well. The flow starts to become influenced by the tail-water depth when the ratio of the tail-water depth to the total head exceeds approximately 0.7. As the ratio increases, the effect on the flow tends to grow dramatically. As shown in this study, a numerical simulation is effective for identifying the stage-discharge relationship of a venturi flume with various types of venturi bodies, including a venturi flume with a circular cone.