We discuss a dual band Complementary Split Ring Resonator (CSRR) based Rectangular Dielectric Resonator Antenna (RDRA). The proposed design operates at 2.3 GHz and 2.6 GHz resonance frequencies respectively. The dual band operation is achieved by using CSRR unit cell in the ground of the proposed antenna along with the Dielectric Resonator (DR). The Dielectric Resonator Antenna (DRA) is excited using a simple microstrip feed line. The 2.3 GHz resonance frequency is obtained by excitation of the CSRR unit cell while the 2.6 GHz resonance frequency is achieved by the excitation of the DRA. The proposed design is simulated using Computer Simulation Technology (CST) software. The antenna has high gain of 6.86 dBi at 2.3 GHz and high gain of 6.4 dBi at 2.6 GHz respectively. Considering the overall performance, the proposed DRA has good characteristics for the WiMAX and LTE wireless applications.