Wave-induced instantaneous liquefaction is crucial to evaluating the stability of offshore foundations. For the instantaneous liquefaction, most previous studies treated the seabed as an invariant poro-elastic medium and hence led to nonphysical tensile stress in the non-cohesive liquefied zone. In this study, a penalty-like dynamic permeability model is proposed, based on the experimental evidences of permeability increase during soil liquefaction. The nonlinearity induced by the dynamic permeability is solved by an iterative procedure, based on the Newton-Raphson method. The numerical procedure is implemented in an in-house code and compared with analytical solutions under the constant permeability assumption. Numerical observations validate that the proposed dynamic permeability model can alleviate or even eliminate the nonphysical tensile stress in the instantaneously-liquefied zone. In contrast to the constant permeability model, the new model with a dynamic permeability obtains a better agreement with existing cylinder tests under one-dimensional wave loading conditions. For the numerical examples presented, the liquefaction depths predicted by constant permeability can be up to twice of those by the new dynamic permeability model. It is concluded that the conventional model with constant permeability overestimates the liquefaction potential.