Local scour around seabed oil, gas or water pipelines can critically affect their stability. Accurate estimation of scour around pipelines is therefore a key topic of research for marine engineers. This paper presents results from a numerical study of clear-water scour depth below a submarine pipeline for a range of steady flow conditions. The flow field around a pipeline under scour equilibrium conditions was numerically simulated by solving the Reynolds-averaged Navier-Stokes equations with the standard k-epsilon turbulence closure. The flow discharge through the scour hole for various flow conditions was then investigated, and the results were used to establish the relationship between the flow discharge and the maximum scour depth. By incorporating the Colebrook-White equation, the bed shear stress was obtained and an iterative method was developed to predict the scour depth around the pipeline. The calculated scour depths using the proposed method agreed well with laboratory measurements, with the average absolute relative error being smaller than that obtained by using previous methods. Therefore, this proposed method can be used to predict the clear-water scour around submarine pipelines with improved accuracy.