Summary: This paper explores the effects of potential function on the saturated liquid and vapor densities of water calculated by pseudo-potential lattice Boltzmann model (PLBM) based on PR equation of state (EOS). By choosing proper potential function form, the simulation results agree well with the Maxwell theoretical values, but there are noticeable differences existing between the simulation results and experimental data. The parameters in PR EOS need modifications. Through analyzing the PR-type EOSs available in literatures, we find from simulations by PLBM that only modifications to the attractive or repulsive parameter in the PR EOS cannot increase the calculation precision of both liquid and vapor density, and at the same time enlarge the applicable temperature range of the PLBM. Therefore, we establish a more accurate PR-type EOS for saturated water and vapor by modifying both the attractive and repulsive parameters in the PR EOS based on PLBM simulations.