Based on Virial Equation of State (V-EOS), a thermodynamic model was developed in this study. The applicability and performance of proposed modified-Virial EOS (mV-EOS) were assessed for calculation of thermodynamic properties of hydrogen and then extended to the hydrogen containing mixtures. For comparison purpose, a number of cubic equations of state were used. Four statistical parameters were defined as goodness criteria which can be regarded as Objective Functions (OF) introduced to optimization method i.e. Black Hole Method (BH). According to obtained results, the model was able to predict the studied thermodynamic properties with desirable accuracy. 2014 Elsevier B.V. All rights reserved.