We present an analytic equation of state (EOS) that describes the three phases of real substances and their transition in a single isotherm. To develop the repulsive contribution of the EOS for the solid-fluid transition, we reinterpret Alder's correlated-cell model (Alder et al. Phys. Rev. Lett. 1963, 11(6), 241) in terms of insertion probability and propose a simple mathematical function for insertion probability which approximately follows that of the correlated cell model. The resulting EOS was found to describe the solid-fluid phase transition of hard-sphere fluids qualitatively, avoiding the solid-fluid critical transition. To extend the model to the solid-vapor and solid-liquid phase transitions, we added the van der Waals attractive contribution to the EOS and tested the combined EOS against the equilibrium properties of eight substances ranging from simple gases to organic compounds. Calculation results show that for eight substances the combined model with four parameters closely reproduces the saturated vapor pressure, predicts the sublimation pressure reasonably, but underestimates the melting pressure, which results from the repulsive contribution of the EOS.