A filling unit to fill a container, in particular a cartridge, with a liquid product of the pharmaceutical industry having: a dosing head, which is arranged in a filling station and is designed to feed a quantity of product into the container through an open upper end of the container; a capping device, which is arranged in a capping station and is designed to insert a closing element into the container and through the open upper end of the container; and a sucking device which is arranged in a degasification station located between the filling station and the capping station, is designed to engage the open upper end of the container in a sealing manner, and is designed to generate a depression inside the container in an upper volume, which is not occupied by the product.