Polyvinylidene fluoride (PVDF)/single-walled carbon nanotube (SWCNT) composites are characterized by X-ray diffraction and scanning calorimetry, and studied by dielectric relaxation spectroscopy (DRS) in the temperature range of −75 to 150 °C. The effects of SWCNTs and SWCNT functionalization are analyzed in terms of α and αc relaxation, dielectric permittivity, loss tangent, and AC electrical conductivity. Some small changes are detected in α relaxation with the addition of SWCNTs, and a strong influence of SWCNTs is observed in the other relaxation αc. Below the percolation threshold, the dielectric permittivity of functionalized SWCNT composites increases compared to blank PVDF, without notable changes in the dielectric loss. All the composite systems show an electrical percolation behavior with different thresholds depending on SWCNT functionalization. Threshold concentrations remain nearly unchanged in the whole temperature and frequency ranges. The base PVDF conductivity strongly depends on temperature and frequency, while the maximum conductivity above the percolation remains nearly unchanged (∼10−2 S/m) for all the systems, temperatures and frequencies.