A two dimensional vertical mathematical model is proposed in this paper for simulating the equilibrium profile of local scour around submarine pipelines. The current model is composed of a new k-ε turbulence model, fitting moving boundary with pre-meshed grid lines and incipient criterion of shear stress for sediments. Employing the proposed model, an instance is carried out numerically and compared with experiments. The calculation results agree well with the experiments. It shows that the improved two-equation turbulence model adopted in this paper is appropriate to simulating the turbulent flow field around submarine pipelines, fitting moving boundary with pre-meshed grid lines method is efficient for moving boundary problems in a multiply-connected domain and the stability evaluation method for seabed with critical shear stress based on log-wall law is a reliable choice.