Enhancing the electrical conductance through amorphous nondoped polymers is challenging. Here, we show that vibrational strong coupling (VSC) of intrinsically nonconducting and amorphous polymers such as polystyrene, deuterated polystyrene, and poly(benzyl methacrylate) to the vacuum electromagnetic field of the cavity enhances the electrical conductivity by at least 6 orders of magnitude compared to the uncoupled polymers. Remarkably, the observed extraordinary conductance is vibrational mode selective and occurs only under the VSC of the aromatic C-H(D) out-of-plane bending modes of the polymers. The conductance is thermally activated at the onset of strong coupling and becomes temperature-independent as the collective strong coupling strength increases. The electrical characterizations are performed without external light excitation, demonstrating the role of vacuum electromagnetic field-matter strong coupling in enhancing long-range transport even in amorphous nonconducting polymers.