A filling machine (6) to fill bottles (1) for products of the pharmaceutical industry having: a filling conveyor (21), which moves a plurality of bottles (1) along a processing path and has a plurality of pockets (25), each designed to house a corresponding bottle (1); a first weighing station (S1) arranged along the processing path and in which the empty bottles (1) are weighed; a filling station (S2) along the processing path and in which a predetermined quantity of product (2) is fed into each bottle (1); and a second weighing station (S3) along the processing path and in which the full bottles (1) are weighed. The filling conveyor (21) has: an annular guide (22), which is arranged in a fixed position along the processing path; a plurality of slides (23), each supporting at least one corresponding pocket (25) and being coupled to the guide (22) so as to freely slide along the guide (22); and a linear electric motor (26), which moves the slides (23) carrying the pockets (25) along the processing path and comprises an annular stator (27), which is arranged in a fixed position along the guide (22), and a plurality of movable sliders (28), each electrically-magnetically coupled to the stator (27) so as to receive, from the stator (27), a driving force and rigidly connected to a corresponding slide (23).