We demonstrate a fully tunable diode structure utilizing a fully suspended single-walled carbon nanotube. The diode's turn-on voltage under forward bias can be continuously tuned up to 4.3 V by controlling gate voltages, which is ∼6 times the nanotube band gap energy. Furthermore, the same device design can be configured into a backward diode by tuning the band-to-band tunneling current with gate voltages. A nanotube backward diode is demonstrated for the first time with nonlinearity exceeding the ideal diode. These results suggest that a tunable nanotube diode can be a unique building block for developing next generation programmable nanoelectronic logic and integrated circuits.