Radio frequency identification is being overloaded with data information, making wideband band antennas very appealing. In this paper, we present a new design of dual band antenna for RFID reader applications operating at 2.45Gz and 5.8GHz with an average gain of 1.16dB at the lower frequency band and 3.2dB at the higher frequency band. The antenna is designed on an FR-4 substrate having a relative dielectric constant of 4.4 and loss tangent of 0.025. The proposed antenna is simulated, designed and, optimized using CST Microwave Studio and has a small size of 32 mm x 26 mm x 1.6 mm. The antenna consists of a steeped rectangular patch antenna using a partial ground plane loaded a modified split ring resonator. The metamaterial structure was designed and optimized to operate at 2.45GHz and its effective parameters was verified using the Nicolson-Ross Weir method. The performance of the proposed antenna is confirmed by another 3D electromagnetic solver HFSS.