Based on the finite volume method, a two-dimensional Computational Fluid Dynamics (CFD) model of local scour of submarine pipeline is established by SST k-ω model, Herschel Bulkley non-Newtonian fluid model and Volume of Fluid (VOF) two-phase flow model, using the pipeline diameter and initial water depth as the variable parameters for the numerical simulation. The characteristics of bed pressure on both sides of the pipeline, scour hole morphology, scour depth duration curve, resistance coefficient duration curve and local velocity distribution of the pipeline are analyzed, and the rule of the influence of pipeline diameter and initial water depth on the local scour characteristics of the submarine pipelines is revealed. The results show that: the local scour of the submarine pipelines in clay seabed environment is significantly affected by pipeline diameter, the larger the diameter of the pipeline, the greater the width and depth of the local scour holes, the further the sediment mound moves to the downstream direction of the pipeline; the initial water depth is of certain influence on the local scour of the submarine pipelines in the clay seabed environment, with the increase of the initial water depth, the local limit equilibrium scour depth of the pipeline decreases, and the downstream bed morphology of the pipeline is obviously affected by the initial water depth.