We report morpho-structural properties and charge conduction mechanisms of a foamy “graphene sponge”, having a density as low as ≈ 0.07 kg/m3 and a carbon to oxygen ratio C:O ≃ 13:1. The spongy texture analysed by scanning electron microscopy is made of irregularly-shaped millimetres-sized small flakes, containing small crystallites with a typical size of ≃ 16.3 nm. A defect density as high as ≃ 2.6×1011 cm−2 has been estimated by the Raman intensity of D and G peaks, dominating the spectrum from room temperature down to ≃ 153 K. Despite the high C:O ratio, the graphene sponge exhibits an insulating electrical behavior, with a raise of the resistance value at ≃ 6 K up to 5 orders of magnitude with respect to the room temperature value. A variable range hopping (VRH) conduction, with a strong 2D character, dominates the charge carriers transport, from 300 K down to 20 K. At T< 20 K, graphene sponge resistance tends to saturate, suggesting a temperature-independent quantum tunnelling. The 2D-VRH conduction originates from structural disorder and is consistent with hopping of charge carriers between sp2 defects in the plane, where sp3 clusters related to oxygen functional groups act as potential barriers.