An automatic transmission of a motor vehicle includes a first rotating element provided by coupling sun gears of a first planetary gear set and a second planetary gear set to each other, a second rotating element provided by coupling carriers of the first and second planetary gear sets to each other, a third rotating element provided by a ring gear of the first planetary gear set, and a fourth rotating element provided by a ring gear of the second planetary gear set. The first rotating element is selectively fixed to a transmission case by a first brake or coupled to an input shaft by a first clutch, and the second rotating element is selectively fixed to the case by a second brake or coupled to the input shaft by a second clutch. The fourth rotating element is coupled integrally to a ring gear of a third planetary gear set, and the third rotating element is coupled integrally to an output gear. With this arrangement, the automatic transmission establishes a selected one of the first-speed through sixth-speed gear stages and a reverse gear stage.