Recently, the demand for millimeter-wave band antenna technology is increasing. We designed a millimeter-wave frequency tuning antenna using the variable dielectric properties of liquid crystal(LC). The liquid crystal can electrically change its phase and has a low-loss characteristic in the millimeter-wave band, so it is suitable for designing a corresponding antenna. We designed a structure capable of injecting liquid crystal into the microstrip patch antenna and applying a DC voltage. The frequency characteristics and radiation pattern of the antenna, which vary according to the change in the liquid crystal dielectric constant, were observed by simulation. When the dielectric constant of the liquid crystal was changed by 0.1, a change in the resonant frequency of about 170 MHz appeared, and the bandwidth at each dielectric constant was 500 MHz or more.