Developing a composite material of polymers and micrometer-sized fillers with higher heat conductance is crucial to realize modular packaging of electronic components at higher densities. Enhancement mechanisms of the heat conductance of the polymer-filler interfaces by adding the surface-coupling agent in such a polymer composite material are investigated through the non-equilibrium molecular dynamics (MD) simulation. A simulation system is composed of α-alumina as the filler, bisphenol-A epoxy molecules as the polymers, and model molecules for the surface-coupling agent. The inter-atomic potential between the α-alumina and surface-coupling molecule, which is essential in the present MD simulation, is constructed to reproduce the calculated energies with the electronic density-functional theory. Through the non-equilibrium MD simulation runs, we find that the thermal resistance at the interface decreases significantly by increasing either number or lengths of the surface-coupling molecules and that the effective thermal conductivity of the system approaches to the theoretical value corresponding to zero thermal-resistance at the interface. Detailed analyses about the atomic configurations and local temperatures around the interface are performed to identify heat-transfer routes through the interface.