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In this paper, a novel numerical wave-current flume is implemented based on the smoothed particle hydrodynamics (SPH) method. The proposed flume is more stable and computationally efficient than conventional ones because it cancels wave paddles or sponge layers while using a non-reflective open boundary condition to simultaneously generate and absorb waves and currents. Numerical tests of nonlinear regular waves interacting with steady currents in the same/opposite directions indicate that the wave-current interactions mainly affect the horizontal velocity distributions in the water body, with little influence on the vertical movements. Water particle trajectories are stretched, and the mass transportation effects are enhanced when the waves and currents are in the same direction. When the directions are opposed, the trajectories, as well as the mass transportation, are compressed, suppressed and even reversed. The applications of solitary wave-current interaction over a submerged bump further show that the relative direction between the wave and the current has remarkable influence on the wave breaking pattern over an underwater obstacle.