In this research a new simple non-attracting hard-sphere equation is introduced. The equation meets the ideal gas and close-packed limits and is in accordance with computer simulation data with reasonable accuracy. When this equation is used with the simplified-perturbed-hard-chain theory equation of state, improvements on the calculation of vapour pressure and saturated liquid density of pure compounds are observed. For 35 pure compounds of different classes, the averages of absolute error are 3.31% and 4.20% for the calculation of vapour pressure and saturated liquid density, respectively. The respected errors for the original equation of state are 3.53% and 4.96%, respectively. Moreover, the use of the new hard-sphere equation in place of the Carnahan-Starling equation in the simplified-perturbed-hard-chain theory equation of state, does not have any appreciable effect on the prediction of K factors in VLE calculations.