Abstract: The invention relates to an anaerobic water purification system, conversion kit and method for treating a liquid. The anaerobic water purification system according to the invention comprises: —a container for the liquid for treatment provided during use with a sludge bed; —a supply conduit operatively connected to the container for supplying the liquid for treatment; —a distribution system connected to the supply conduit for distributing the liquid over the sludge bed from above; —carrier material which is arranged during use in the container and to which anaerobic sludge material can attach; and—a gas roof arranged at or on the container and provided with a volume which can be adapted during use to the biogas production. The carrier material is preferably free-floating material. The discharge conduit for discharge of treated liquid is preferably connected to a riser pipe.