We demonstrate controllable and gate-tunable negative differential resistance in carbon nanotube field-effect transistors, at room temperature and at 4.2 K. This is achieved by effectively creating quantum dots along the carbon nanotube channel by patterning the underlying, high-kappa gate oxide. The negative differential resistance feature can be modulated by both the gate and the drain-source voltage, which leads to more than 20% change of the current peak-to-valley ratio. Our approach is fully scalable and opens up a possibility for a new class of nanoscale electronic devices using negative differential resistance in their operation.