The PVTx properties of the H2O-CO2-H-2 mixtures have significant applications in the technology of supercritical water gasification of coal. Here, we first carry out the molecular dynamics simulations of the PVTx properties of the H2O-CO2-H-2 mixtures in the near critical and supercritical regions of water to generate 600 datasets at 750-1150 K and 4.0 -443.5 MPa. The molar fraction of each composition in the ternary mixtures ranges from 10% to 80%. Later we investigate the applicability of a well-known thermodynamic model for the ternary mixtures, namely the Duan-Moller-Weare equation of state (DMW EOS). It is observed that the DMW EOS shows great potential in the prediction of the PVTx properties of the ternary mixtures. However, it is noted that the mixing parameters describing the binary interactions of H2O-H-2 and CO2-H-2 are still unknown in the DMW EOS. By determining the missing mixing parameters using the Levenberg-Marquardt algorithm, the accuracy of the original DMW EOS is improved for the ternary mixtures. Moreover, optimizing the coefficients in the DMW EOS further promotes the accuracy of the model for the H2O-CO2-H-2 mixtures. The results from this work may facilitate the development of supercritical water gasification of coal. (C) 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.