Molecular dynamic (MD) simulations were carried out to predict the thermo-mechanical properties of the cured epoxy network composed of diglycidyl ether bisphenol A (DGEBA) epoxy resin and tetrahydrophthalic anhydride (THPA) curing agent and their single-walled carbon nanotubes (SWCNT) reinforced the epoxy matrix composites. Different characters such as the density of the materials and mean square displacements (MSDs) were calculated to estimate the glass transition temperatures (Tgs) of of the materials. 365 K and 423 K of the Tgs were obtained respectively, whereas the latter is much higher than the former. The simulation results indicated that the incorporation of SWCNTs in the epoxy matrix can significantly improve the Tg of the cured epoxy. The approach presented in this study is ready to be applied more widely to a large group of candidate polymers and nanofillers.