AlN/GaN double-barrier resonant tunneling diodes (DB-RTDs) were fabricated on (0001) Al2O3 substrates by molecular-beam epitaxy, using a rf-plasma nitrogen source. The AlN/GaN DB-RTDs were designed to have a 3-ML-thick GaN quantum well and 4-ML-thick AlN barrier layers sandwiched by Si-doped n-type GaN contact layers. The current-voltage characteristics of mesa diode samples showed clear negative differential resistance (NDR) at room temperature. The NDR was observed at 2.4 V with a peak current of 2.9 mA, which corresponds to 180A/cm2. A peak-to-valley current ratio as high as 32 was obtained.