In this study, the effect on the conductance of polymer nanocomposites considering quantum tunneling resistance is investigated with respect to the chirality of carbon nanotubes (CNTs) and uncertainties in the geometric parameters of CNTs by using Monte Carlo simulations. The random spatial placement for CNTs was accomplished with a one-dimensional line segment and the periodic boundary conditions were applied to CNTs in the two-dimensional representative volume element. Intersection points between each CNT were calculated to obtain connectivity lists of the connected network path. Both the intrinsic resistance of the CNT and the inter-CNT tunneling resistance were considered in this model. In addition, the in-house code developed was validated by comparison with several experimental datasets from the literature. Unlike past studies, uncertainties in the chiral index of single-wall CNTs concerning armchair and zig-zag structures have been considered here and the electrical conductivity and percolation threshold are predicted.