In this paper, a stereoscopic ultra-wideband (UWB) Yagi–Uda (SUY) antenna with stable gain by near-zero-index metamaterial (NZIM) has been proposed for vehicular 5G communication. The proposed antenna consists of magneto-electric (ME) dipole structure and coaxial feed patch antenna. The combination of patch antenna and ME structure allows the proposed antenna can work as a Yagi–Uda antenna, which enhances its gain and bandwidth. NZIM removes a pair of C-notches on the surface of the ME structure to make it absorb energy, which results in two radiation nulls on both sides of the gain passband. At the same time, the bandwidth can be enhanced effectively. In order to further improve the stable gain, impedance matching is achieved by removing the patch diagonally; thus, it is able to tune the antenna gain of the suppression boundary and open the possibility to reach the most important characteristic: a very stable gain in a wide frequency range. The SUY antenna is fabricated and measured, which has a measured −10 dBi impedance bandwidth of approximately 40% (3.5–5.5 GHz). Within it, the peak gain of the antenna reaches 8.5 dBi, and the flat in-band gain has a ripple lower than 0.5 dBi.