A new and distinct Stevia rebaudiana plant named ‘SW 129’ is described. The new variety is distinguished from other Stevia varieties by high plant vigor high plant yield late flowering excellent sweet leaf taste with very low bitterness and aftertaste and leaves having a high rebaudioside A, a high percentage of rebaudioside A to total steviol glycosides, and a high ratio of rebaudioside A content to stevioside content.
