5G cellular networks will require providing significantly higher system capacity and user data rates. This potential growth along with today’s shortage of spectrum increases the need for new frequency spectrum. The new millimeter wave spectrum is emerging as a suitable candidate with a large amount of available bandwidth (around 60 GHz). The new spectrum places a new requirement for single element antenna and array design. This paper addresses the issues of mm-wave antenna design and the problems that designers may face during the designing process. The proposed antenna has a resonating frequency of 26 GHz and 2 GHz bandwidth. Beam squint problem is also analysis in this paper. The results showed that the gain of the mm-wave antenna array becomes a function of frequency which significantly reduces the performance of mm-wave communication system. Millimeter wave (mmWave) wireless technology has become a part of human life for high-speed and secure data transmission. This paper proposed a square microstrip patch antenna at 26GHz resonant frequency for mmWave wireless communication. The antenna consists of one square radiating element. The proposed antenna has been designed and investigated on Rogers RO 3003 lossy substrate with relative permittivity 3 using Electromagnetic Simulation Software CST Microwave Studio. The result of this paper shows minimal return loss −19.34 dB, gain 6.97dBi, and bandwidth 2GHz at 26 GHz resonant frequency. The element is converted to a uniform linear array of 8 elements the proposed array increases the gain to 16dBi with high radiation efficiency.