Amidst escalating data traffic demands, the fifth generation (5G) of mobile communication has been launched to curb these demands by providing high data rates, decreased latency, increased network capacity and large bandwidth. The ambitious performance expected from the 5G cellular communication network is enabled by different key technologies including shifting towards the millimeter wave frequency band. However, the millimeter wave band is accompanied by limitations of signal path loss and propagation loss due to small wavelengths. As a result, antenna arrays with high antenna gain are used to mitigate these signal path and propagation losses without consuming more power and at a low cost. Antenna arrays have a shortfall of having a limited angular coverage due to narrow beams. As such, phased array antennas are adopted to provide electronic beam steering in desirable directions. This thesis proposes an eight element phased array antenna for 5G wireless applications. The proposed antenna is designed to operate in the millimeter wave band specifically at 28 GHz. Antenna element or radiating element is an important aspect in designing a phased array antenna, in this thesis a single rectangular patch antenna is used as a radiating element. Three single patch antennas are designed using three dielectric substrates. After antenna performance comparison, the single patch antenna designed using RT 5880 dielectric substrate was chosen as the radiating element for the proposed eight element phased array antenna. The proposed phased array antenna is composed of two 1 ⇥ 4 array antenna which are fed by two excitation ports and phase shifting is introduced at these ports to achieve beam steering. From the simulation results, the proposed phased array antenna achieved reflection coefficient of -40.19 dB, bandwidth of 1.51 GHz, antenna gain of 15.92 dBi, scan angle of ±41 and mutual coupling effect in the array is -27.97 dB. To reduce mutual coupling, a dumbbell shaped defected ground structure (DGS) is inserted in the array and a mutual coupling reduction of 6.27 dB is achieved. In conclusion, the proposed phased array antenna has a limited scan angle and the insertion a dumbbell shaped DGS in the array reduced mutual coupling and increased the bandwidth of the antenna. However, the insertion of DGS did not improve antenna parameters related to radiation pattern as there is a decrease in antenna gain and directivity.