A multi-stage apparatus for continuous waste water filtration, comprises a first tank (12) provided with a waste water inlet pipe (14) to supply water containing suspended solids to the tank and a large diameter outlet pipe (26); a second tank receiving the mixture from the outlet pipe, the second tank being sufficiently large to allow settling of the larger suspended solids and being provided with a lower, openable port (36) for discharge of settled solids and having an upper weir (50) for discharge of partially-cleared water; and a continuously-driven, perforated belt (44), having a surface positioned to receive, at a first location, a stream of the discharged, partially-cleared water, the belt perforations being sized to enable the passage of clear water therethrough while retaining fine solids on the surface for subsequent discharge at a second location, a water collection trough being provided under the first location for water passing through the belt perforations, and a solids collection bin being provided at the second location, for collection of particles falling off the belt at the second location. The invention also provides a method for continuous filtration of waste or potable water.