A simple and scalable method to fabricate graphene-cellulose paper (GCP) membranes is reported; these membranes exhibit great advantages as freestanding and binder-free electrodes for flexible supercapacitors. The GCP electrode consists of a unique three-dimensional interwoven structure of graphene nanosheets and cellulose fibers and has excellent mechanical flexibility, good specific capacitance and power performance, and excellent cyclic stability. The electrical conductivity of the GCP membrane shows high stability with a decrease of only 6% after being bent 1000 times. This flexible GCP electrode has a high capacitance per geometric area of 81 mF cm−2, which is equivalent to a gravimetric capacitance of 120 F g−1 of graphene, and retains >99% capacitance over 5000 cycles. Several types of flexible GCP-based polymer supercapacitors with various architectures are assembled to meet the power-energy requirements of typical flexible or printable electronics. Under highly flexible conditions, the supercapacitors show a high capacitance per geometric area of 46 mF cm−2 for the complete devices. All the results demonstrate that polymer supercapacitors made using GCP membranes are versatile and may be used for flexible and portable micropower devices.