In this Letter, an investigation is performed on the utilization of nematic liquid crystal (NLC) cells in the design of leaky-wave antennas (LWAs) for millimeter-wave (mm-wave) radiation in order to dynamically control its beam scanning capability at a single frequency. A NLC compound is sandwiched between two single-sided copper-plated substrates allowing a traveling wave to be guided through a substrate-integrated waveguide. The tuning capabilities of the structure, based on the use of K15 or GT7-29001 as the middle layer, were evaluated for different biasing conditions demonstrating the associated dynamic scanning of the main beam. A quasi-periodic LWA was designed to operate in the 5G mm-wave band, thus supporting a fast-wave propagation with tunable phase constant and dynamic beam steering at a single frequency. The simulated results clearly illustrate a dynamic beam scanning range of 45° through the use of an external bias voltage ranging between 0 and 40 V. These results are quite promising creating a fertile ground for the utilization of NLCs in the design and fabrication of LWAs for 5G wireless communication networks.