An investigation of the relationship between the microstructure parameters and thermomechanical properties of epoxy resin can provide a scientific basis for the optimization of epoxy systems. In this paper, the thermomechanical properties of diglycidyl ether of bisphenol A (DGEBA)/methyl tetrahydrophthalic anhydride (MTHPA) and DGEBA/nadic anhydride (NA) were calculated and tested by the method of molecular dynamics (MD) simulation combined with experimental verification. The effects of anhydride curing agents on the thermomechanical properties of epoxy resin were investigated. The results of the simulation and experiment showed that the thermomechanical parameters (glass transition temperature (Tg) and Young’s modulus) of the DGEBA/NA system were higher than those of the DGEBA/MTHPA system. The simulation results had a good agreement with the experimental data, which verified the accuracy of the crosslinking model of epoxy resin cured with anhydride curing agents. The microstructure parameters of the anhydride-epoxy system were analyzed by MD simulation, including bond-length distribution, synergy rotational energy barrier, cohesive energy density (CED) and fraction free volume (FFV). The results indicated that the bond-length distribution of the MTHPA and NA was the same except for C–C bonds. Compared with the DGEBA/MTHPA system, the DGEBA/NA system had a higher synergy rotational energy barrier and CED, and lower FFV. It can be seen that the slight change of curing agent structure has a significant effect on the synergy rotational energy barrier, CED and FFV, thus affecting the Tg and modulus of the system.