The submarine pipeline, known as the “lifeline of the sea”, undertakes the important task of safe transportation of oil, natural gas and other resources. However, due to the enhanced hydrodynamics in the vicinity of the submarine pipeline, large scale pipeline foundations laid on clay seabed are susceptible to local scour, causing the soil beneath the pipeline to be hollowed out, which leads to the phenomenon of overhanging in the submarine pipeline. Suspension spans are a major cause of failures in submarine pipelines. Therefore, it is crucial to conduct research on the local scour characteristics of submarine pipelines. Existing studies on local scour of submarine pipelines have mainly focused on the local scour characteristics of submarine pipelines in sandy seabed environment, and more comprehensive research results have been obtained. However, there are few reports about the impact of pipeline diameter and initial water depth on the local scour characteristics of submarine pipelines in a clay seabed environment. The diameter and initial water depth of the pipeline respectively affect the local Reynolds number and pressure of the pipeline, Reynolds number and pressure are key parameters which affect local scour of the pipeline. Therefore, the local scour characteristics of pipelines with different diameters under different initial water depth environments are studied, the development process, depth and hydrodynamic characteristics of local scour holes in different scale submarine pipelines are systematically analyzed, it is helpful to further improve the relevant theories and guide engineering practice of submarine pipeline scour in clay seabed environments. In this paper, a two-dimensional CFD model of local scour of submarine pipeline is established by using Herschel-Bulkley clay model and VOF two-phase flow model, the pipeline diameter D and initial water depth h as variable parameters for numerical simulation, the law of influence of pipeline diameter and initial water depth on local scour characteristics of submarine pipelines is revealed. The results show that: (1) The local scour of submarine pipelines in clay seabed environment is significantly affected by pipeline diameter. The larger the diameter D 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. (2) The initial water depth will have a certain influence on the local scour of 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, the downstream bed morphology of the pipeline is obviously affected by the initial water depth.