The invention relates to a floating platform for harnessing wind energy, comprising a tower (1) with a wind turbine (2), and two horizontal, identical cylindrical floating elements (3) parallel to the main longitudinal axis of alignment, the tower and the floating elements being interconnected by bar structures (5). The floating elements are joined to a stabilising element (4) which is situated directly beneath the floating elements (3), said stabilising element comprising two substantially rectangular first concrete slabs (4a), which are solid or more lightweight, with a ribbed structure, arranged perpendicularly to the axes of the floaters and joined to said floaters by means of auxiliary structures.