A.Gordon first studied solitonic coductivity in some hydrogen-bonded ferroelectric materials, using the hydrogen-bonded chain model with asymmetric double-well potential, and gave the kink solution and expression for its mobility. However, kink solitons making contribution to proton-solitonic conductivity should be the solitons corresponding to proton transfer between two wells. For this reason, we suggest revising Gordon’s result, giving a low-energy-state kink solution and a new expression for its mobility. With the asymmertic double-well potential transforming to the symmetric one, this expression is reduced exactly to the same form as previous research result. This expression shows that the phase-transision critical index is 1.