Tailoring and assembling graphene into functional macrostructures with well-defined configuration are key for many promising applications. We report on a graphene-based woven fabric (GWF) prepared by interlacing two sets of graphene micron-ribbons where the ribbons pass each other essentially at right angles. By using a woven copper mesh as the template, the GWF grown from chemical vapour deposition retains the network configuration of the copper mesh. Embedded into polymer matrices, it has significant flexibility and strength gains compared with CVD grown graphene films. The GWFs display both good dimensional stability in both the warp and the weft directions and the combination of film transparency and conductivity could be optimized by tuning the ribbon packing density. The GWF creates a platform to integrate a large variety of applications, e.g., composites, strain sensors and solar cells, by taking advantages of the special structure and properties of graphene.