To sustain the pace with immense prominence, interest in low-loss terahertz (THz) waveguides increases due to their particular applications in the multidisciplinary arena. This paper narrates a novel solid-core polymer-based square lattice micro-structured optical fiber (SL-MOF) with circular air-holes for efficient propagation of THz waves. The anticipated model’s guiding attributes are described by employing the numerically efficient finite-element method (FEM) in conjunction with an auxiliary Ring Model. Numerical analysis of the model exhibits confinement loss of about ~ 10 -7 dB/cm and low effective material loss of ~ 0.19 cm -1 at the applied frequency of 1.0 THz. It is also demonstrated that the considered geometry furnishes low bending loss over the extended range of THz frequency. The relative sensitivity coefficient is evaluated in context for the targeted design parameters to enable the said model’s practical utility. Other nameworthy propagation characteristics, such as effective mode-index, power fraction, effective mode-area, numerical aperture, spot-size, and the beam divergence are also investigated. The improved outcomes are anticipated that the proposed configuration will be opened a new epoch in the THz waveband.