Frequency-induced instability is widely present in nematic liquid crystals (LCs), which poses a problem in improving liquid-crystal-based phase-shift devices driven by alternating currents. Herein, the Fréedericksz transition of thick nematic LCs was investigated under alternating electric fields to reveal the suppression of frequency-induced instability in the low frequency range. By extending the Frank-Leslie equation to the AC-driven case, the response of the LC was numerically calculated, and the frequency threshold for suppressing the driven instability was estimated in conjunction with the perturbation method. Experimentally, the frequency suppression of LC fluctuations was verified by using applied electric fields. In addition, the root-mean-square-error of the refractive index was measured to be less than 2 × 10-5, which excludes the convective instability-generating domains in devices. It was revealed that the fabricated thick LC phase shifters provided a phase shift of more than 360° at 2 THz and can be used in the terahertz band. It was observed that the electrically driven phase-shift characteristics were in accordance with the theoretical results as the threshold frequency condition was satisfied. This work provides an experimental and theoretical reference for improving modulation performance and enhancing the characterization of AC-driven LC-based phase-shift devices.