In this study, a reflective terahertz dual-band linear polarization converter based on a metasurface structure is proposed. It adopts a typical "sandwich" structure. The upper and lower layers are metal layers, and the middle layer is a dielectric layer. Efficient conversion of x-polarized waves to y-polarized waves is realized. The results show that the polarization conversion rate of the polarization converter can reach more than 90% in the frequency bands of 0.611?0.713 THz and 1.335?1.364 THz. In the frequency bands of 0.626?0.677 THz and 1.340?1.360 THz, the polarization conversion rate is close to 100%, and perfect linear polarization conversion is realized. Using the surface current distribution, its polarization switching mechanism is elucidated in detail. The polarization conversion rate calculated based on the interference model theory agrees well with the simulation value. The polarization converter has a simple structural design, is easy to process, and has broad application prospects in the fields of terahertz communication, imaging, and detection.