A discrete KleinGordon model with asymmetric potential that supports kinks free of the PeierlsNabarro potential (PNp) is constructed. Ratchet of kink under harmonic AC driving force is investigated in this model numerically and contrasted with the kink ratchet in the conventional discrete model where kinks experience the PNp. We show that the PNpfree kinks exhibit ratchet dynamics very much different from that reported for the conventional lattice kinks which experience PNp.