Millimeter wave (mmWave) communication systems have become a potential candidate to deliver ultrahigh data throughput, e.g., 10 Gb/s owing to congestion in low frequency bands and requirements of high data throughput. According to FCC rules, 28, 37, 39 and 64-71 GHz bands have been suggested for next-generation wireless communication; in addition, Wireless Gigabit (WiGig) alliance also operates at an unlicensed 60 GHz band. Therefore, according to these proposed or developed wireless communication standards, we need multiband mmWave antennas. In this study, an antenna with a quasi-Yagi structure that consists of three arms and six spiral directors is proposed. To miniaturize the antenna, each arm plays multiple roles simultaneously, which include a driver, a reflector, a director, and/or an impedance matching network. In addition, the spiral directors are able to improve the antenna gain and enhance the impedance matching bandwidth at 60 GHz, simultaneously. The proposed antenna is compact (5 × 8 × 0.203 mm3) and the measurement results show that the antenna covers major 5G millimeter-wave bands (26.5-29.5 and 37-40 GHz) and the WiGig band (57-67 GHz). The measured peak gains of the proposed antenna are 6.2, 7.56 and 9.42 dBi, which correspond to 28, 38 and 60 GHz, respectively. The measured results confirm the good performances observed by electromagnetic simulations. The proposed mmWave triband antenna is suitable for mobile devices satisfying mmWave 5G and WiGig applications.