This work presents a simple stacked rectangular dielectric resonator antenna (RDRA), which is dedicated for ISM band applications. To design this RDRA antenna, an EM simulator has been used. The proposed structure consists of a dielectric resonator, which is mounted on plastic substrate. This resonator is fed using a simple aperture-coupled feed line over a rectangular feeding slot made on a copper ground plane. The substrate has a relative permittivity of 2.65 and tan 0.025. The proposed antenna has a compact size of 49.5x49.5x1.63. The physical dimensions of the dielectric resonator are 30 mm, 30 mm, and 35 mm for the length, width, and height, respectively. The dielectric resonator of the proposed stacked RDRA has two layers. The first layer is constructed using plastic dielectric, which is used for the construction of our substrate. However, the second layer is fabricated using FR-4, which has a relative permittivity of 4.4 and tan 0.025. Due to the using of the second layer in our proposed stacked RDRA, an enhancement in the gain has been obtained, with a peak gain up to 5 dB and an efficiency up to 95% over the desired ISM band. In Addition, the obtained radiation pattern presents high stability over the operating frequency band.