A new simple extended corresponding-states principle has been developed to represent and predict the thermophysical properties of fluids. The extended corresponding-states principle only requires the substance-dependent critical parameters and acentric factor which enhances the corresponding-states principle of Pitzer et al. to include the behavior of substances whose force fields deviate strongly from spherical symmetry. The additional corresponding-states parameter defined in terms of the deviation of the critical compression factor of a real molecule from that of spherical molecules is independent of experimental data for any specific property. The new simple extended corresponding-states principle presented here remarkably improves the representation of the vapor pressure from the triple point to the critical point and the second virial coefficient from the triple point to the highest temperatures over which experimental data exist. Accurate results for these two well-understood properties are given for simple, normal, polar, hydro-bonding and associating compounds. The results also show that the new simple extended corresponding-states principle is more reliable and accurately predicts the vapor pressure and second virial coefficient of a strongly nonspherical fluid than any other existing methods.