A terahertz single-polarization single-mode (SPSM) fiber with tunable polarization is proposed based on the index-matching coupling method. The asymmetric microstructure is designed in fiber core to split the x and y polarized core modes. The index matching liquid is filled into the air-hole of the fiber cladding, so that the x or y polarized core modes match the defect mode. The matching switch between the two polarized modes is realized by changing the refraction index of filled liquid. The results show that the x polarized mode matches when the refractive index of the liquid is 1.288. When the frequency of the incident light is higher than 0.73 THz, the polarization loss ratio of the fiber is bigger than 100, and the optical fiber operates in y-polarization mode. At the frequency of 1 THz, the polarization loss ratio reaches the maximum of 1020. The y polarized mode matches when the refractive index of the liquid is 1.338. From 0.87 THz to 0.93 THz, the polarization loss ratio of the fiber is bigger than 100, and the optical fiber operates in x-polarization mode. At the frequency of 0.9 THz, the polarization loss ratio reaches the maximum of 118. This design has realized the switch of the single fiber polarization operation mode, and has features such as broadband, tunable and easy to fabricate.