Although much progress has been made to develop high-performance lithium-sulfur batteries (LSBs), the reported physical or chemical routes to sulfur cathode materials are often multistep/complex and even involve environmentally hazardous reagents, and hence are infeasible for mass production. Here, we report a simple ball-milling technique to combine both the physical and chemical routes into a one-step process for low-cost, scalable, and eco-friendly production of graphene nanoplatelets (GnPs) edge-functionalized with sulfur (S-GnPs) as highly efficient LSB cathode materials of practical significance. LSBs based on the S-GnP cathode materials, produced by ball-milling 70 wt % sulfur and 30 wt % graphite, delivered a high initial reversible capacity of 1265.3 mAh g-1 at 0.1 C in the voltage range of 1.5-3.0 V with an excellent rate capability, followed by a high reversible capacity of 966.1 mAh g-1 at 2 C with a low capacity decay rate of 0.099% per cycle over 500 cycles, outperformed the current state-of-the-art cathode materials for LSBs. The observed excellent electrochemical performance can be attributed to a 3D "sandwich-like" structure of S-GnPs with an enhanced ionic conductivity and lithium insertion/extraction capacity during the discharge-charge process. Furthermore, a low-cost porous carbon paper pyrolyzed from common filter paper was inserted between the 0.7S-0.3GnP electrode and porous polypropylene film separator to reduce/eliminate the dissolution of physically adsorbed polysulfide into the electrolyte and subsequent cross-deposition on the anode, leading to further improved capacity and cycling stability.