We have investigated properties of a plastic photonic crystal fiber guiding terahertz radiations, THz photonic crystal fiber. The single-mode condition and dispersion of a plastic triangular THz photonic crystal fiber are investigated by using the plane wave expansion method and the beam propagation method. The THz photonic crystal fiber can perform as a single-mode fiber below 2.5 THz when the ratio of diameter (d) and period (${Lambda}$) of air holes is less than 0.475. The THz photonic crystal fiber with ${Lambda}=500{mu}m$ and $d/{Lambda}=0.4$ shows almost zero flattened dispersion behavior, $-0.03{pm}0.02 ps/THz{cdot}cm$, in the THz frequency range from 0.8 to 2.0 THz.