Planar interconnected graphene woven fabrics (GWFs) are prepared by template-based chemical vapor deposition and the GWFs are employed as multi-functional filler for epoxy-based composites. Apart from flexibility, transparency, lightweight and high electrical conductivity, the GWFs have unique morphological features consisting of orthogonally interweaved, inherently percolated, hollow graphene tubes (GTs). The orthogonal GT structure means that the GWF/epoxy composites hold significant anisotropy in mechanical and fracture properties. The composites with 0.62 wt.% graphene deliver a combination of excellent electrical and fracture properties: e.g. an electrical conductivity of ~0.18 S/cm; and fracture toughness of 1.67 and 1.78 MPa·m1/2 when loaded along the 0° and 45° directions relative to the GT direction, respectively, equivalent to notable 57% and 67% rises compared to the solid epoxy. Unique fracture processes in GWF/epoxy composites are identified by in situ examinations, revealing crack tip blunting that occurs when the crack impinges GTs, especially those at 45 to the crack growth direction, as well as longitudinal tearing of hollow GTs as the two major toughening mechanisms.