A hybrid electrode material for high-power supercapacitors was fabricated by grafting carbon nanofibers (CNFs) onto the surface of powdered activated carbon (AC) through catalytic chemical vapor deposition (CCVD). A uniform thin layer of disentangled CNFs with a herringbone structure was deposited on the carbon surface through the decomposition of propane at 450 °C over an AC-supported nickel catalyst. CNF coating was controlled by the reaction time and the nickel content. The superior CNF/AC composite displays excellent electrochemical performance in a 0.5 mol L−1 solution of K2SO4 due to its unique structure. At a high scan rate (100 mV s−1) and current loading (20 A g−1), the capacitance values were three- and fourfold higher than those for classical AC/carbon black composites. Owing to this feature, a high energy of 10 Wh kg−1 was obtained over a wide power range in neutral medium at a voltage of 0.8 V. The significant enhancement of charge propagation is attributed to the presence of herringbone CNFs, which facilitate the diffusion of ions in the electrode and play the role of electronic bridges between AC particles. An in situ coating of AC with short CNFs (below 200 nm) is a very attractive method for producing the next generation of carbon composite materials with a high power performance in supercapacitors working in neutral medium.