A carbon nanotube (CNT) capacitor includes a CNT film and four terminals. The first terminal includes a first end electrode disposed at a first end of the CNT film. The second terminal includes a second end electrode disposed at a second end of the CNT film. The third terminal includes an upper electrode disposed above the CNT film. The fourth terminal includes a lower electrode disposed below the CNT film. A method of operating a CNT capacitor includes applying a first signal across the first and second terminals to switch a CNT film from a conductive state to a non-conductive state, and applying a second signal across the third and fourth terminals to store charge or to discharge charges in the CNT capacitor. A method of making a CNT capacitor includes providing four terminals and a CNT film.