We report the design and preparation of graphene and polyaniline (PANI) woven-fabric composite films by in-situ electropolymerization. The introduction of PANI greatly improves the electrochemical properties of solid-state supercapacitors which possess capacitances as high as 23 mF/cm^2, and exhibit excellent cycling stability with ~100% of capacitance retention after 2000 cycles. The devices have displayed superior flexibility with improved areal specific capacitances to 118% during deformation.