A new method was proposed by combining the Corresponding-States Theorem with the Group-Contribution Method (CSGC) and a new vapor-pressure equation was developed for estimating purpose. Group-contribution parameters of 117 functional groups were obtained by correlating 6540 datum points of experimental vapor pressures for 462 compounds, including alkanes, alkenes, cyclohydrocarbons, aromatics, halogenated hydrocarbons and compounds containing oxygen, sulfur and nitrogen etc. Predicted results for vapor pressures of 28 compounds show that the proposed equation with the normal boiling point temperature T(b) only is superior to the conventional Corresponding-States Methods. Furthermore, satisfactory results were also obtained by the proposed equation in estimating high vapor pressures of several compounds.