The present invention provides a lithium ion battery anode material comprising a submicron-scaled graphitic fibril having a diameter or thickness less than 1 μm but greater than 100 nm, wherein the fibril is obtained by splitting a micron-scaled carbon fiber or graphite fiber along the fiber axis direction. This type of graphitic fibril exhibits exceptionally high electrical conductivity, thermal conductivity, elastic modulus, and strength. The anode material exhibits a high reversible capacity and good charge/discharge cycling stability for both low and high charge rate conditions. Another preferred embodiment of the present invention is an anode active material containing a graphitic fibril with a diameter greater than 1 μm but less than 6 μm obtained by splitting a carbon fiber or graphite fiber of at least 6 μm in diameter.