A simplified perturbed hard-chain theory (SPHCT) equation of state is used to predict the vapour-liquid equilibria of 69 one-component fluids including n-alkanes, n-alkenes, n-alkynes, n-alkanols, polyatomic polar molecules and noble gases. A procedure is reported for obtaining the equation of state parameters from critical properties and the acentric factor. The predicted vapour pressures are compared with experimental data over a wide range of temperature, which in many cases, extends from the triple point to the critical point of the fluid. The calculations are also compared with results obtained using the Christoforakos-Franck equation of state. It is concluded that the hard-chain theory methodology represents vapour-liquid equilibria of non-spherical molecules more accurately than hard-sphere approaches. The average absolute deviation in the vapour pressure predicted by the SPHCT equation of state is typically within the range of 5%-15%.