<p>A design of a switchable dual-mode linear-to-circular polarization converter (LTC-PC) in the terahertz (THz) band is reported based on vanadium dioxide (VO₂). Adjusting the VO₂ state allows the converter to alternate between the transmission and reflection modes. In the insulating state, VO₂ enables transmission mode operation for a forward x- or y-polarized wave. LTC polarization conversion occurs within the frequency bands of 1.26–1.47 THz and 1.83–1.85 THz. Moreover, this mode yields an LTC polarization conversion at a frequency of 1.7 THz. The polarizer operates in reflection mode when VO₂ is in the metallic state. Two conversion bands are identified for circular polarization within the frequency bands of 0.93–1.67 THz and 1.80–1.86 THz. The dual-mode polarization converter achieves axial ratios below 3 dB and a polarization conversion efficiency greater than 0.8. Surface current distributions reveal the polarization conversion mechanisms. Furthermore, we analyze the polarization ellipses of both reflected and transmitted waves at various frequencies across the operational bands. We anticipate that the proposed design, featuring high performance and dual functionality, will be applicable in THz communication systems and sensors.</p>