This paper represents an exact modeling for auto-transformer (AT)-fed ac high-speed railroad (HSR) using constant current mode. AC HSR has rapidly changing single-phase load, and at a feeding substation, three-phase electric power is transformed to the paired directional single-phase electric power. As the train moves along a section of line between two adjacent ATs, analysis of the catenary voltage in AT-fed ac HSR system is a quite complicated work. Therefore, in order to solve this complicated system, this paper proposes a novel and efficient method with generalized equations for the catenary voltage of AT-fed ac HSR. The voltage profile through the entire railroad system can be solved regardless of the number and position of trains, feeding distance from substation, and normal or extension mode. In the case studies, the results of the proposed equation for the catenary voltage profile are compared with those of the simulation using PSCAD/EMTDC.