This letter introduces a novel high-gain, dual-polarized magneto-electric dipole (ME-dipole) antenna that incorporates a compact dual-polarized ME-dipole director for the first time. The innovative director uses a crossed open cavity with four horizontal metal plates mounted on its open ends, resulting in dual-polarized magnetic and electric dipole directors. The antenna is fed by two cross-positioned Γ-shaped probes of varying heights, providing ± 45° polarization. The measured impedance bandwidths for Port 1 and Port 2 are 34.63% (2.34 - 3.32 GHz) and 36.03% (2.23 - 3.21 GHz), respectively, with a 31.35% overlap. The antenna achieves an average gain of 13.7 dBi for Port 1 and 13.6 dBi for Port 2, with peak values of 14.13 dBi and 14.07 dBi, respectively. Compared with the conventional dual-polarized ME-dipole antenna without loading a director, the proposed design achieved a gain enhancement of more than 4.6 dB. Furthermore, high isolation of over 20 dB between the two ports and a stable radiation pattern and an impressive front-to-back ratio are maintained. These features make the proposed antenna an excellent choice for use in 5G communication systems.