The tetrachalcogenide TaTe4 is known as an excellent example of a charge-density wave (CDW) system that has a commensurately modulated structure at room temperature. Using density function perturbation theory, we find that the unmodulated phase of TaTe4 has a giant Kohn anomaly at room temperature, which manifests itself as softened phonon modes at the CDW vector (1/2a*,1/2b*,1/3c*). Interestingly, after the application of 8 GPa hydrostatic pressure, this CDW instability can be effectively suppressed and disappears at room temperature. By studying the topology of the Fermi surface and the phonon linewidth, we show that the Kohn anomaly in TaTe4 is driven by a large electron–phonon coupling coefficient at the CDW vector and not by Fermi surface nesting.