Cover for a swimming pool or whirlpool bath, whereby the cover includes a rollup screen whereby the screen has two side edges and whereby the screen has a first edge perpendicular to the side edges and a second edge perpendicular to the side edges, whereby the cover includes a rollup shaft, whereby the first edge of the screen is connected to the rollup shaft and whereby the screen can be rolled up and rolled out on the rollup shaft, whereby the rollup shaft is horizontally movable so that the screen can be rolled out while the second edge is in a fixed position and whereby the cover is provided with a unit to exert a rotational force on the rollup shaft to thereby roll up the screen.
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