  A discrete Klein-Gordon model with asymmetric potential that supports kinks
free of the Peierls-Nabarro potential (PNp) is constructed. Undamped ratchet of
kinks under harmonic AC driving force is investigated in this model numerically
and contrasted with the kink ratchets in the conventional discrete model where
kinks experience the PNp. We show that the PNp-free kinks exhibit ratchet
dynamics very much different from that reported for the conventional lattice
kinks which experience PNp [see, e.g., Phys. Rev. E {\bf 73}, 066621 (2006)].
Particularly, we could not observe any significant influence of the
discreteness parameter on the acceleration of PNp-free kinks induced by the AC
driving.
