In the aeon of nanotechnology, size is concern. Proposed, the design is focused on miniaturized the size of micropatch patch antenna. In this design, firstly design a microstrip patch antenna at resonating frequency 3.304 GHz. After that, the antenna design with the planned “Interconnected hexagonal rings” of double negative material structure, due to this cover of double negative material structure the antenna is start resonating at frequency 2.088 GHz.. For designing an antenna at resonating frequency 2.088 GHz is required more space than the design . The resonating frequency decreases when the size of antenna is increased. The purpose of this design, the size of antenna is constant and still managed to decrease the resonant frequency. In the design, the micropatch patch antenna (MPA) is incorporated with the double negative material cover which has some special properties so the antenna is miniaturized the size 60%, return loss reduces 247%, VSWR improves 41% and radiation efficiency also improves 36% . The purpose of this work is to design a compact, improve its return loss, radiation efficiency and VSWR all simulated results are analyzed by using computer simulation technology microwave studio software(CST-MWS) 2010