Nanoscale surface engineering is playing important role in enhancing the performance of battery electrode. VO2 is one of high-capacity but less-stable materials, and has been used mostly in the form of powders for Li-ion battery cathode with mediocre performance. In this work, we have designed a new type of binder-free cathode by bottom-up growth of bi-face VO2 arrays directly on a graphene network for both high-performance Li-ion and Na-ion battery cathodes. More importantly, graphene quantum dots (GQDs) are coated onto the VO2 surfaces as a highly efficient surface "sensitizer" and protection to further boost the electrochemical properties. The integrated electrodes deliver a Na storage capacity of 306 mAh g-1 at 100 mA g-1, and a capacity of more than 110 mAh g-1 after 1500 cycles at 18 A g-1. Our result on Na-ion battery may pave the way to next-generation postlithium batteries.