An open-cell model equation of state has been proposed, which relaxes the restrictions of the cell theory and allows more flexibilities in describing the structure of liquids. To test its capability, this equation has been applied to a variety of liquids, including 17 heavy molecular weight hydrocarbons, 10 organic solvents, and 15 polymers, in particular. The calculated density grand average AADp for the equation proposed here are 0.062, 0.057, and 0.054 per cent against the results for the equation of state by Simha and Somcynsky, 0.081, 0.093, and 0.072 percent for the above three groups of liquids, respectively. Good agreement between our calculated results and experimental data indicates that our model is an improvement over the Simha and Somcynsky equation of state, which has been evaluated as one of the best equations. Moreover, this equation can be easily extended to describe the properties of polymer solutions and polymer blends, which will be addressed in our subsequent paper.