We demonstrate the nonvolatile resistive switching of an amorphous carbon (a-C) layer with carbon nanotube (CNT) electrodes for ultra-dense memory. The use of CNT as electrode leads to the ultimately scaled cross-point area (~1 nm 2 ), and the use of a-C results in an all-carbon memory. Carbon-based complementary resistive switching (CRS) is shown for the first time, enabling cross-point memory without cell selection devices.