A Rectangular Microstrip Patch Antenna with “Quadruplet circular hollow rings” shaped metamaterial cover is designed and replicate at a height of 3.2 mm from the ground plane. The antenna along with the proposed metamaterial cover is designed to resonate at 2.21 GHz frequency (in S-Band). But the proposed metamaterial cover significantly reduces the return loss and increases the bandwidth and efficiency of the antenna in comparison to rectangular microstrip patch antenna alone. The proposed antenna is suitable for application of WLAN requiring 34 MHz bandwidth space and reduced return loss, of about –23.58 dB and its efficiency increases by 62.84% (approx. 21%). Hence there is reduction in frequency which refers to reduction of size of the antenna. The scope of this paper is to design and simulate the proposed artificial structure with simultaneous negative permittivity and permeability or the so-called Left Handed Metamaterial. Nicolson-Ross-Weir approach has been used for verifying the double-negative properties of the proposed metamaterial.