A Dual band rectangular dielectric resonator antenna (RDRA) capable of fre- quency tunings at two different resonant modes is presented and investigated. In this design two rectangular dielectric resonators with different permittivity situated on top of the substrate are employed. The antenna is fed by 50 Ω microstrip feedline etched on the top of the Fr-4 epoxy printed circuit board (PCB) with a total size of 80 × 50 × 1.6 mm3 and εrs = 4.6 (loss tangent = 0.02). In order to excite two resenant frequencies, two RDRA with relative permittivity of εr1 = 10 and εr2 = 30 are chosen to operate at 2.4 GHz and 3.8 GHz. From the parametric study the lower permitivity DRA resonates at 3.8 GHz whereas the higher permitivity DRA resonates at 2.4 GHz. Ansoft HFSS v14 has been used for the simulation of the proposed dual-band an- tenna. The simulation results show that the 3.8 design can efficiently perform in both frequency bands.