A series of tunable negative differential conductance regions at room temperature is demonstrated in semiconducting carbon nanotubes suspended over a trench with a metallic gate at its bottom. The substrateless carbon nanotube is in fact a wide quantum well that experiences a series of negative differential conductance regions due to the very large difference between the effective masses in the well and the tunneling contacts. The positions of these regions can be tuned by modifying the gate voltage. Since the negative differential conductance is the key element of high-frequency oscillators, the suspended nanotube is a voltage-controlled oscillator able to work up to THz frequencies. This device could have important applications in high-frequency nanoelectronic devices and multivalued logic.