The millimeter-wave spectrum plays a vital part in 5G communication, e.g., the n258 band is recommended to achieve ultra-high-speed data for mobile phones. However, most current patch antennas currently used in 5G mobile devices cannot cover the entire spectrum (n258). In this study, a new type of patch antenna model for the n258 band used in mobile phones has been designed and simulated in CST. Rogers RT5880 material was used as a substrate to deliver higher working frequency and broader bandwidth. Based on the simulations, the S1-1 curve is lower than -10dB from 24.25~27.5GHz for each antenna with dimensions of 9.5 × 9.0 × 1.1(mm). Besides, the realized gain is above 6.3dB in the same band by HFSS simulations. Meanwhile, its performance would be further improved when this kind of antennas form an array. These results indicate that this antenna’s dimension and performance meet the operating requirements of 5G mobile phones. Additionally, it is proved that the antenna array has the function of enhancing gain and directivity. Furthermore, the analysis substantiates those available materials with lower dielectric constants should be developed for a substrate. These results shed light for future patch antennas designed in 5G mobile devices.