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In this paper, the smoothed particle hydrodynamics (SPH) method is used to build a numerical wave-current tank (NWCT). The wave is generated by using a piston-type wave generator and is absorbed by using a sponge layer. The uniform current field is generated by simultaneously imposing the directional velocity and hydrostatic pressure in both inflow and outflow regions set below the NWCT. Particle cyclic boundaries are also implemented for recycling the Lagrangian fluid particles. Furthermore, to shorten the time to reach a steady state, a temporary rigid-lid treatment for the water surface is proposed. It ts out to be very effective for weakening the undesired oscillatory flow at the beginning stage of the current generation. The calculated water surface elevation and horizontal-velocity profile are validated against the available experimental data. Satisfactory agreements are obtained, demonstrating the good capability of the NWCT.