© 2019 Elsevier B.V. The rapid development of portable and wearable electronics requires novel flexible energy storage devices with high energy and power densities. Nevertheless, the fabrication of high-performance flexible electrodes for achieving this goal remains challenging. We herein report a large-area and highly-flexible polymer-derived silicon oxycarbide ceramic (SiOC) fibers cloth modified by quasi three-dimensional graphene framework (3D-GNS/SiOCf) as a flexible anode for lithium ion batteries (LIBs). The SiOC fibers have a hierarchical porous structure and a rough surface to facilitate the insertion/extraction of Li+ ions, while the GNS framework provides a conductive network by bridging the adjacent SiOC fibers and coating the individual SiOC fibers to significantly enhance electron transfer and robust electrochemical Li+ ion storage. Therefore, this 3D-GNS/SiOCf material exhibits a high reversible capacity (924 mAh g-1 at 0.1 A g-1), good rate performance (330 mAh g-1 at 2.0 A g-1), and excellent cycling stability (686 mAh g-1 at 0.5 A g-1 after 500 cycles). A prototype flexible LIB full cell assembled using this anode with LiFePO4 cathode exhibits good performance through a series of bending tests. Consequently, the resultant 3D-GNS/SiOCf anode has great potential for flexible energy storage and sheds light on the design of other flexible devices.