Prediction of wave-induced instantaneous (oscillatory or momentary) liquefaction is particularly important for the design of offshore foundations. Most previous studies applied the linear Darcy model to characterize the porous flow in a seabed. This treatment was found to cause fallacious tensile stresses in a non-cohesive seabed. In this study, to overcome such shortcomings of previous models, a non-Darcy flow model is proposed based on a Karush–Kuhn–Tucker (KKT) condition. In the KKT condition, the primal constraint arises from the fact that the tensile behavior does not exist in a non-cohesive seabed, while the dual condition arises from the physical evidences that the pore-fluid velocity increases during liquefaction. The non-linearity of the present model is handled by the Newton–Raphson method within the standard finite element framework, without coding constrained variational principle. This highlights the convenience for numerical implementation. The difficulties in treating the nonlinearity by previous dynamic permeability model are also eliminated by the non-Darcy flow model. The merits of the proposed model are validated by examining four numerical treatments and two liquefaction criteria. The liquefaction depth by the present model is found to be roughly 0.73 times of the value by the linear Darcy model.