In this paper, combination of electromagnetic band gap (EBG) and split-ring resonator (SRR) loads with fractal formation for miniaturization of microstrip antenna is noticed. Here two different shapes of antenna have been studied with two well-known metamaterial structures as parasitic elements. A conventional microstrip antenna, which is surrounded by four EBG unit cells, is chosen as the first antenna. It has an effective resonance at 2.5. The Minkowski fractal method is applied to EBG unit cells in this stage. The Minkowski fractal structure is implemented for accession of effective capacitance in EBG unit cells. The second antenna frequencies are 2.5 and 5.9 GHz. It contains a slot structure with four SRRs, used for making parasitic elements and for achieving multi-band characteristic. The fractal method is used to improve the inductance of SRR structure by increasing the effective length of microstrip line. At this stage, the applied fractal structure has been modified, so that the frequency of wireless application could be achieved. In the last step, by some changes in feed line of the slot antenna, circular polarization (CP) is obtained for the second antenna, which shows that SRR load can be helpful for making the CP.