A novel dual-wideband dual-polarised magnetoelectric (ME) dipole antenna for the fourth generation (4G)/fifth generation (5G) microcell base station is proposed. Using a pair of orthogonal ME dipoles and Γ-shaped tapered cross feeding lines, the initial antenna achieves dual-band and dual-polarised. Then, four U-shaped gaps, added in electric dipoles, effectively extend the lower impedance bandwidth. Finally, a circular parasitic patch with capacitive properties is innovatively loaded above the ME antenna, which obviously reduces the high-resonant frequency from 5.5 to 4.9 GHz. Meanwhile, a box-shaped reflector is employed to achieve stable gain and radiation patterns. As a result, the measured results show the good dual-wideband performance of 52.4% (2.14–3.66 GHz) and 7.4% (4.68–5.04 GHz) with voltage standing wave ratio (VSWR) 25 dB) and high gain (9.5 and 5.5 dBi, respectively). In addition, a stable radiation pattern with a half-power beam width of 63.5 ° ± 6.8 ° and good cross-polarisation discrimination (>20 dB) on the E-plane is realised over these two bands.