In this study, the theoretical investigation of the electrically heated catalyst(EHC) for vehicle application has been carried out using the thermal equivalence of EHC system and the data of vehicle tests to meet ultra low emission vehicle(ULEV) standard. To improve the efficiency of EHC system, it is necessary to understand relation between the power, the operating time and the conversion efficiency of EHC system. The relation was found with thermal equivalence of EHC system which considers the power supply to EHC, heat loss, chemical exothermic energy generated by oxidation reaction and net energy coming in via the exhaust gas. From this relation, the limits of needful power and operating time to meet the ULEV standard can be suggested, when the conversion efficiency of catalyst was known.