We have performed the first-principles calculation on a ferroelectrics phenazine-chloranil acid (Phz-H(2)ca), which includes an asymmetric hydrogen bond O-H (center dot center dot center dot) N. These hydrogen bonds play the role of building bridges for electronic wave functions between molecules instead of proton tunneling. The charge density in this intermolecular region strongly enhances the electric polarization by the shift of the Wannier function centers, which is described by the Berry phase. It is found that the small molecular distortion enhances the covalency between molecules. This extended nature of electronic wave functions is crucial to the hydrogen-bonded ferroelectrics, which has been ignored in the conventional picture.