Fabrication of high-performance nanocomposites requires that the nanoscale fillers be dispersed uniformly and form a continuous network throughout the matrix. Direct infiltration of porous CNT sponges consisting of a three-dimensional nanotube scaffold may provide a possible solution to this challenge. Here, we fabricated CNT sponge nanocomposites by directly infiltrating epoxy fluid into the CNT framework while maintaining the original network structure and CNT contact, with simultaneous improvement in mechanical and electrical properties. The resulting composites have an isotropic structure with electrical resistivities of 10 to 30 Ω·cm along arbitrary directions, much higher than traditional composites by mixing random CNTs with epoxy matrix. We observed reversible resistance change in the sponge composites under compression at modest strains, which can be explained by tunneling conduction model, suggesting potential applications in electromechanical sensors.