In this paper, using finite element method, we design a novel photonic crystal fiber which acts as a terahertz (THz) silicon waveguide. We study the important transmission properties, namely, group velocity dispersion (GVD), absorption coefficient, effective mode area and effective nonlinearity by varying the core diameter and distance between two consecutive airholes for a wide range of frequency from 0.5 to 10THz. The proposed THz silicon PCF exhibits three zero dispersions at 1.75, 4.8 and 7.8 THz frequencies. Further, we report a low absorption coefficient of 10-4 cm-1 in a broad frequency region (2.5 to 10THz). We obtain a large mode area of 325 mm2 at 0.5THz frequency for the core diameter of 0.9mm and the pitch of 3mm. These results show that the proposed THz silicon PCF (THz-SPCF) would turn out to be a good candidate for THz waveguide compared to other plastic THz waveguides.