COMSOL Multiphysics simulation software has been used to create a hexagonal photonic crystal fiber (H-PCF) with hexagonal cladding and a rotating hexa elliptical shape core. The hexagonal photonic crystal fiber (H-PCF) fiber is built on five layers of circular air holes, and it is suitable for telecommunication applications especially optical fiber communication in the terahertz (THz) frequency range. The hexagonal photonic crystal fiber (H-PCF) is designed to have an ultra-low effective material loss (EML), a higher core power fraction, a bigger effective area, and reduced confinement loss. The smallest effective material loss from the proposed hexagonal photonic crystal fiber (H-PCF) is 0.00689 cm−1, with a better core power fraction of 82%, less confinement loss of 3.45 × 10–14 cm−1 and a better effective area of 3.65 × 10–4 m2 is achieved at one terahertz (THz) waveguide region. Furthermore, using the features of the V-Parameter, our developed hexagonal photonic crystal fiber (H-PCF) fiber reveals an optical waveguide with one mode throughout a frequency range of terahertz (THz) wave area. So, it has been said that our hexagonal photonic crystal fiber (H-PCF) structure will be highly beneficial for optical fiber communications applications in the THz frequency range.