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Nanoelectronic devices based on ferroelectric domain walls (DWs), such as memories, transistors, and rectifiers, have been demonstrated in recent years. Practical high-speed electronics, on the other hand, usually demand operation frequencies in the giga-Hertz (GHz) regime, where the effect of dipolar oscillation is important. In this work, an unexpected giant GHz conductivity on the order of 103 S/m is observed in certain BiFeO3 DWs, which is about 100,000 times greater than the carrier-induced dc conductivity of the same walls. Surprisingly, the nominal configuration of the DWs precludes the ac conduction under an excitation electric field perpendicular to the surface. Theoretical analysis shows that the inclined DWs are stressed asymmetrically near the film surface, whereas the vertical walls in a control sample are not. The resultant imbalanced polarization profile can then couple to the out-of-plane microwave fields and induce power dissipation, which is confirmed by the phase-field modeling. Since the contributions from mobile-carrier conduction and bound-charge oscillation to the ac conductivity are equivalent in a microwave circuit, the research on local structural dynamics may open a new avenue to implement DW nano-devices for RF applications.