This article presents the design of a microstrip patch antenna at different frequencies above 20 GHz that intended to be used for fifth generation (5G) telecommunication system. The design of microstrip patch antenna that has a radiating element with a rectangular shape and partial ground plane is proposed. The patch antenna is designed using a Rogers RT5880 substrate with dielectric constant, <em>ε<sub>r</sub></em> of 2.2. The results of the designed antenna design analyzed in terms of the reflection coefficient, bandwidth, gain, and directivity performance. The proposed patch antennas at design frequencies of 25.875 GHz, 38.75 GHz, 43 GHz, 46.25 GHz, 48.7 GHz, 51.5 GHz, 71 GHz, and 83.5 GHz have a fractional bandwidth, gain and directivity that respectively greater than 10.2 %, 2.159 dB and 2.562 dBi. All designs and analysis are performed by using the CST Microwave Studio software.