A computational model is developed to study the thermal conductivity of single-walled carbon nanotube (SWNT)-polymer composites. An off-lattice Monte Carlo simulation was used to model the effects of interfacial resistance at the SWNT-polymer interface and at the SWNT- SWNT contact on the heat flow for different orientations of SWNTs dispersed in the polymers. A primary focus is the non-isotropic heat conduction in aligned-SWNT polymeric composites that are of interest for various heat conduction applications such as microelectronic heat sinks, and also because this geometry constitutes a representative volume element (RVE) of CNT-reinforced polymer matrices in hybrid advanced composites under development. The simulation is an extension of a previous model for heat transfer in nanocomposites in that it now considers SWNT-SWNT contact. The simulation results of the developed model are compared with those of the previous model. The effects of SWNT orientation, SWNT-SWNT contact, weight fraction and thermal boundary resistance on the effective conductivity of composites are quantified. The present model is a useful tool for the prediction of the thermal conductivity within a wide range of volume fractions of the SWNTs, including the case when SWNTs are in contact with each other.