In recent years, the interfacial thermal resistance has been an attracting research topic since optimization of thermal transport across interface is important in various applications in industry. The mechanism of the thermal transport across interface should be pursued from the nanoscopic scale; however, obtaining the thermal resistance is usually implemented under non-equilibrium condition by molecular dynamics simulation. Generally, the calculation of the thermal resistance at a specific temperature is difficult by using such non-equilibrium molecular dynamics (NEMD) simulation. Recently, the equilibrium molecular dynamics simulation (EMD) method has been proposed in the calculation of thermal resistance, but the details on this method are still not clear. In this study, we adopted two equilibrium molecular dynamics simulation methods to investigate thermal resistances at various interfaces and made the comparisons with the traditional non-equilibrium molecular dynamics simulation method. The two methods adopted were based on the auto-correlation function using the heat flux and instantaneous temperature difference, respectively. After comparisons, it was found that the calculation results obtained by the two methods under EMD simulation had a strong consistency, although there was a slight deviation when compared them with the result obtained by NEMD simulation.