In these days, with the improvement of wireless and mobile communication, Wi-Fi technology is everywhere in life. When wireless communication standards are examined, it is observed that 2.4 GHz (2.4-2.4835 GHz) and 5 GHz (5.15-5.825 GHz) frequency bands are used as the Wi-Fi frequency band. Therefore, in this paper, a microstrip Wi-Fi antenna design with dual band performance at 2.4 GHz and 5 GHz frequencies has been achieved. Thanks to the choice of microstrip antenna. It will be ensured that the proposed antenna has the advantageous features of microstrip antennas compared to other antennas. The feed of the antenna will realize with a microstrip line. FR-4 substrate is used as dielectric material with a thickness of 0.8 mm. Thanks to the preferred materials and cheap production cost, fabrication of the antenna is considered. The CST Studio Suite is preferred by the world's largest technology and engineering companies, as it provides a market advantage over the products by providing a shorter development period and lower cost. The design stages of the antenna have been carried out using CST Studio Suite. Also, important parameters of the antenna have been examined and optimized bandwidth, input impedance, resonance frequency, reflection coefficient, return loss, etc. As a result, dual-band Wi-Fi antenna design has been determined with wide bandwidth and high gain.