A novel numerical technique for simulating interfacial gravity waves is considered. The model comprises an immiscible, binary fluid lattice Boltzmann model incorporating a gravitational interaction and simulates two immiscible, viscous fluids of different densities with a sharp interface between them. The model is described and the accuracy of the technique is considered. Simulation results are presented and the wave velocities, the oscillation frequency and the damping rate are found and compared to theory. A good comparison is found suggesting that the lattice Boltzmann approach is indeed accurately mimicking the wave dynamics.