In order to study the frequency characteristics of flapping motion of submerged impinging jet, a submerged plane jet impinging onto a free surface is investigated based on the free energy lattice Boltzmann method for a given water depth. It is verified that there exists a new flapping impinging pattern, in addition to the stable impinging pattern. The PSD analyses at specific positions of flapping jet show that the lateral velocity u and surface displacement oscillate with the same frequency. And the frequency of longitudinal velocity oscillation at the jet centerline is twice of that of the transverse oscillation. Meanwhile, the mean centerline velocity decay is considerable faster than that of the stable impinging jet without flapping motion.