Predicting the thermal conductivity of loose-fill fibrous thermal insulation is a complex problem, when considering the combined conduction, convection, and radiation heat transfer within a scattering, emitting, and absorbing medium. A piecewise model for predicting the overall apparent thermal conductivity of large diameter opaque fibrous materials was developed by considering the radiation heat transfer, solid conduction and air conduction components separately. The model utilized the physical parameters of emissivity, the density of the solid fiber material, the percentage composition and range of fiber diameter, and the mean fiber diameter to develop specific equations for piecewise contribution from radiation, solid fiber conduction, and air conduction toward the overall effective thermal conductivity. It can be used to predict the overall apparent thermal conductivity for any opaque fibrous specimen of density (ρ), known thickness (t), mean temperature (T), and temperature gradient (ΔΤ). Thermal conductivity measurements were conducted in accordance with ASTM C518 specifications on 52 mm thick, 254 mm square test specimens for coconut and sugarcane fibers. The test apparatus provided results with an accuracy of 1%, repeatability of 0.2%, and reproducibility of 0.5%. The model was applied to and compared with experimental data for coconut and sugarcane fiber specimens and predicted the apparent thermal conductivity within 7% of experimental data over the density range tested. The model also predicted the optimum density range for both coconut and sugarcane fibers.