A machine for making filter bags (1) with infusion products comprises: a feed station (3) for a continuous web (S) of filter paper; a station (4) for forming and joining the continuous web (S) in a closed tubular shape which is fed along a vertical feed axis (Z); a station (5) for filling the product with a pusher element (9) able to move along the vertical feed axis (Z); a station (6) for joining an open lower end of the continuous tubular web (S) forming, alternately, the bottom end (F) and the top end (T) of individual filter bags (1); a handling and control unit for the bottom end (F) able to move in such a way that it is synchronized with the joining station (6) along the vertical feed axis (Z) for pulling the web of filter paper (S) and controlling the position of the bottom end (F) of the filter bag (1) being formed.