Specially constructed cylindrical carriages have been used to ensure that passengers can stay upright.
The floors tilt, adjusting to the slope as the funicular climbs 110m (360ft) over a distance of 100m at the steepest point.
The railway runs from the town of Schwyz up to the car-free Alpine village of Stoos.
The Stoos Bahn took 14 years to build - two years longer than scheduled - at a cost of 52m Swiss francs (£40m; $53m).
But Ivan Steiner, spokesman for the railway, said the project's completion had made everyone "very proud".
In mountainous Switzerland, where children regularly use cable cars to get to school, the line will connect communities as well as provide a new tourist attraction, reports the BBC's Imogen Foulkes.
Should potential passengers feel fainthearted, they can be reassured that the journey lasts just four minutes.
(Video courtesy : BBC News)