An apparatus for making spunbonded nonwoven has a spinneret for emitting the continuous filaments in a filament-travel direction, a cooling chamber downstream in the direction from the spinneret and receiving the filaments, and two air-supply manifolds flanking the chamber for feeding cooling air thereinto transverse to the direction. A flow straightener for equalizing flow of the cooling air on the filaments is provided in at least one of the air-supply manifolds and has passage walls forming a plurality of flow passages that extend transversely to a filament-travel direction. A flow cross section of the flow straightener is greater than 85% (preferably more than 90%) of a cross-sectional size of the straightener, a ratio of a length L of the flow passages to an inner diameter Di of the flow passages L/Di is 1 to 15.