Terahertz communication technology holds promise for solving the challenging “blackout” problem. Research has revealed that the spectrum exhibits new peaks when terahertz waves propagate through plasma. In the realm of communications, elucidating the underlying physical mechanisms responsible for these novel peaks is of paramount importance. In this paper, a combination of theoretical analysis and simulation is utilized to investigate the causes of these spectral changes. Theoretically, the expression for the relative dielectric constant of plasma has been refined by incorporating collision terms. Drawing on radiation theory, a particle whose motion is interrupted by collisions can be considered equivalent to a damped harmonic oscillator. Thus, the frequency expression of the new peak was derived. Furthermore, the simulation involved the interaction of a terahertz wave, which had a frequency of 1 THz and lasted for 2 ps, and plasma characterized by a central electron density of 1021 m−3 and a collision frequency of 0.114 THz. The simulation results are consistent with the frequency expression of the new peak. In sum, this study found that collisions between electrons and neutral particles within plasma cause a shift in the frequency of terahertz waves, and has derived the frequency expression. This plasma model can be used to estimate the frequency range of terahertz waves that are generated as they propagate through collisional plasmas.