Gain and bandwidth enhancement of low profile, linearly polarized square dense dielectric patch antennas using a frequency selective surface (FSS) superstrate layer is proposed. A high dense dielectric patch antenna is utilized as a radiating element instead of a metallic patch in order to gain several significant advantages, including low profile, wide bandwidth, and high radiation efficiency. The implemented antenna is excited by an aperture-coupled feeding technique. The antenna gain is enhanced by using a highly reflective FSS superstrate layer, realizing an antenna gain enhancement of 11 dBi. The implemented antenna acquired a measured gain of about 17.78 dBi at 28 GHz with a 9% bandwidth and radiation efficiency of 90%. The bandwidth of the proposed antenna is improved by using a unit cell printed on two sides, as it provides a positive phase gradient over the desired frequency range. The antenna impedance bandwidth is broadened and the measured impedance matching S11 exhibited a 15.54% instead of 9% bandwidth while maintaining a high-gain characteristic of about 15.4 dBi. The implemented antenna presents a solid radiation performance with good agreement between the measured and simulation results. For some attractive advantages such as low profile, low cost, lightweight, small size, and ease of implementation, the proposed antenna is a very good candidate for millimeter-wave wireless communications.