Local scour around submarine pipelines can affect the stability of the pipeline. The accurate estimation of the scour around submarine pipelines has been a hot topic of research among marine engineers. This paper presents results from a numerical study of clear-water scour depth below a submarine pipeline for a range of the steady flow conditions. The flow field around the pipeline under scour equilibrium condition is numerically simulated by solving the Reynolds-Averaged Navier-Stokes (RANS) equations with the standard k-ε turbulence closure. The flow discharge through the scour hole for various flow conditions is investigated. The results are used to establish the relationship between the flow discharge and the maximum scour depth. Incorporated with the Colebrook-White equation, the bed shear stress is obtained and an iterative method is proposed to predict the scour depth around the submarine pipeline. The calculated scour depths using the present method agree well with the laboratory measurements, with the average absolute relative error being smaller than that using previous methods, indicating that the proposed method can be used to predict the clear-water scour around the submarine pipeline with satisfactory accuracy.