Electrically conductive polymer composites (CPCs) with bendable and stretchable deformation capacity are one of key challenges for flexible cable, wearable electronics and so on. 3D graphene network is an emerging graphene bulk material beyond the pre-exiting graphene powders and films, which is also an advanced 3D-network filler instead of traditional powdery fillers, for the construction of CPCs. Herein, a strutted-graphene foam is produced at large scale, whose shape is customizably designed. The strutted graphene is further applied as the filler for making a composite. The fabricated composite shows comprehensively enhanced mechanical modulus, thermal conductivity, and electrical conductivity, which increase by 40%, 54%, and 8 orders of magnitude at a low filling fraction of 0.15 vol% of strutted graphene, respectively. The fabrication process is facile, low-cost, and scalable, which can be envisaged as a rational design and engineering of advanced polymeric composites.