In the emerging technology field of printed electronics, circuits are envisioned to be powered with printed energy sources, such as printed batteries and printed supercapacitors (SCs). For manufacturing and reliability issues, solid electrolytes are preferred instead of liquid electrolytes. Here, a solid-state, polyanionic proton conducting electrolyte, poly(styrenesulfonic acid) (PSS:H), is demonstrated for the first time as an effective ion conducting electrolyte medium in SCs with electrodes based on carbon nanotube (CNT) networks. The effect of the ionic conductivity in the PSS:H film of those SCs is studied at different levels of relative humidity (RH) with impedance spectroscopy, cyclic voltammetry, and galvanostatic charge-discharge techniques. High capacitance values (85 F g−1 at 80% RH) are obtained for these SCs due to the extremely high effective electrode area of the CNTs and the enhanced ionic conductivity of the PSS:H film at increasing RH level. The charging dynamics are primarily limited by the ionic conductivity of the electrolyte rather than a poor contact between the electrolyte and the CNT electrodes. The use of polyelectrolytes in SCs provides high mechanical strength and flexibility, while maintaining a high capacitance value, enabling a new generation of printable solid-state charge storage devices.