A process for the treatment of waste water containing heavy metals in which sulphur components and/or metals are biologically reduced to precipitate the metals as water-insoluble metal species, which are separated from the waste water. The biological reduction and the precipitation of the metal species are carried out in a moving sand bed, in which sand particles partly immobilize the bacteria and retain the precipitated metal species, treated waste water is separated from the precipitated metal species and the precipitated metal species are subsequently separated from the sand particles. Metals like selenium and uranium can be precipitated without sulphur components, whereas metals like antimony, cadmium, copper, zinc and the like are precipitated as sulphides.