The present work proposes a novel design of a dual-band-printed antenna for operation at the millimeter-wave frequencies 28 and 38 GHz that are utilized for the modern and future generations of mobile communications. The antenna is composed of two radiating elements. The first element is the main patch that is fed through a microstrip line with inset feed, and the second element is a parasitic element that is fed through capacitive coupling with the main patch. The design parameters of the proposed antenna are optimized through a complete parametric study to give excellent impedance matching at 28 GHz over the band 27.7–28.3 GHz and at 38 GHz over the band 37.7–38.3 GHz. The surface current distributions at the two operational frequencies are investigated. The designed antenna is used to construct a four-port efficient multi–input–multi–output (MIMO) system. The MIMO system performance is investigated regarding the envelope correlation coefficient (ECC), diversity gain (DG), and the channel capacity loss (CCL) showing very good performance. The single-element antenna and the MIMO are fabricated and experimentally evaluated showing excellent impedance matching over the lower and higher frequency bands, which come in agreement with the simulation results. It is shown that the antenna produces maximum gain of 7.4 and 8.1 dBi at 28 and 38 GHz, respectively. The average radiation efficiencies of the proposed antenna are 88% and 88.8% over the lower and higher frequency bands, respectively. In addition, the coupling coefficients between the MIMO antenna systems are measured experimentally showing very low coupling values resulting in an efficient MIMO system that is suitable for future millimeter-wave (mm-wave) applications.