Nowadays, the high gain and compact antennas are the most common issue that commonly considered by many researchers in the telecommunication area, especially in antenna design. There are many types of microstrip patch antenna had been researching to cater this problem. This paper is focused on the combination of defected microstrip structure of split ring resonators (DMS-SRR) and defected ground structure of split ring resonators (DGS-SRR) on the ground plane. The proposed DMS-SRR structure effect to wider the bandwidth and also increase the gain of the Minkowski fractal patch antenna. The other technique used in this design is a double layer substrate of FR-4 to improve the gain of the antenna. This double layer effect to increase the Minkowski fractal antenna gain to 3.827 dB, but it shifted the resonant frequency to 2.634 GHz. The DGS-SRR structure used to shift back the resonant frequency to 2.4 GHz region. Other parameters that had been considered in this work are return loss, radiation pattern and surface current. The first work is started by designing a normal Minkowski patch antenna. Then, three units of DMS-SRR had been added to the front side of the Minkowski fractal antenna. After that, a pair of DGS-SRR had been added to the ground plane of the antenna. The resonant frequency of this antenna is 2.4 GHz used for wireless LAN (WLAN) application. The proposed antenna capability to improve the antenna gain from 2.445 GHz to 3.650 GHz while the bandwidth is improving from from 69.00 MHz (2.368 GHz to 2.437 GHz) to 129.90 MHz (2.407 GHz to 2.537 GHz).