An index-guiding novel solid-core photonic crystal fiber (SC-PCF) formed by a hexagonal lattice of circular-shaped air holes arranged in silicon background is realized. By varying the radius ‘r’ of the air holes from 0.1a to 0.5a (where ‘a’ is defined as the lattice constant), the characteristic electromagnetic modes of the low loss Terahertz (THz) fiber were solved through eigenmode analysis using finite element method (FEM). The effective mode area and the nonlinearity of the proposed PCF are calculated for different radii of the air holes and it is found that the effective mode area decreases when the radius of the air holes is increased. On the other hand, the nonlinearity increases for an increase in the air holes radii. At 1 THz, the confinement loss of the proposed fiber is in the order of 10−23 dB/m and transmittance efficiency above 96% has been attained. As 5-G technology emanates, THz wave propagation becomes essential and the designed hexagonal lattice SC-PCF will be useful for the advancement of communication systems, sensing devices and several medical applications.