The fifth generation (5G) mobile communications systems demand millimeter wave (mmWave) bands of the electromagnetic spectrum beside the current sub-6 GHz frequencies. Allocation of mmWave frequencies for the cellular systems will ensure more capacity and higher speed links. For the last few years wireless communications societies in industry and academia have put significant research effort to develop novel and efficient antenna architectures. We need brand-new antenna structures that can overcome the challenges of 5G communications environment such as high propagation loss of mmWaves and the large bandwidth demand of the planned networks. In this paper, a microstrip mmWave antenna array for 5G mobile phone terminals is introduced. First, the single antenna element with the rectangular patch radiator is investigated. The numerical investigation is carried out with a full-wave electromagnetic solver. The single antenna design operates between 27.1 GHz – 28.95 GHz frequencies. The proposed antenna based on microstrip approach shows low profile characteristics without compromising performance. A maximum gain of ~7.7 dBi is achieved within the operation band. Then eight-element phased array implementation of the proposed antenna is analyzed. Uniformly spaced linear array method is used with ~λ/2 spacing in the configuration. The eight-element array boosts the maximum total gain value up to ~ 15 dBi, and yields beam steering at broadside up to ∓50° with low side lob levels (SLL). Furthermore, the proposed phased array design is compact with the dimensions of 10 mm×48.6 mm×0.51 mm, and therefore it is compatible with the mmWave band radio frequency integrated circuit (RFIC) transceivers.