This paper proposes a novel antenna structure that simultaneously satisfies high gain, dual-polarization, and fan-beam radiation pattern characteristics for Private 5G base stations in next-generation railway communications. In Private 5G railway communications, a balance of high gain, dual-polarization, and fan-beam is crucial. High gain and fan-beam pattern maximize coverage along the track, while dual-polarization provides link robustness for high-speed mobility. The proposed antenna element achieves a high gain of 12.8 dBi and stable radiation performance despite its relatively compact size by employing a radiation mechanism based on a higher-order mode patch antenna and a sidelobe suppression technique utilizing central and side slots. Furthermore, by rotating the antenna by 45 \(^\circ\) and configuring it in a slant dual-polarization structure, it provides robustness against polarization variations that frequently occur in practical communication environments. A 6 \(\times\) 1 array antenna constructed based on the proposed antenna element forms a stable fan-beam radiation pattern with suppressed grating lobes even at wide array spacing of 1.27 \(\lambda _0\) , providing a horizontal half-power beamwidth (HPBW) of 6 \(^\circ\) , a vertical HPBW of 38 \(^\circ\) , and a peak gain of 18.6 dBi. The 6-way power divider designed for dual-polarization array feeding ensures excellent uniform power distribution with an insertion loss deviation within ± 0.32 dB and an insertion phase deviation within ± 2.8 \(^\circ\) . Both the proposed antenna element and the array antenna achieve sufficient bandwidth coverage for the Private 5G band, demonstrating performance suitable for application in practical base station environments. Moreover, a figure-of-merit comparison defined based on peak gain, fractional bandwidth, and antenna size confirms that the proposed antenna achieves the most balanced performance compared to previously reported high gain dual-polarized antennas. These results indicate that the proposed antenna can provide high reliability for next-generation Private 5G railway base stations and offer significant advantages in terms of coverage, interference mitigation, and link robustness in practical railway operating environments.