A device for holding and carrying along a substrate to be printed on, for a printing machine, comprising: a conveyor (3) comprising an endless belt (8) formed by hollow box structures (9) extending transversely and having a flat outer face and comprising means for driving the belt and means (19a) for guiding the box structures. The flat outer faces (17) of the box structures circulate over a flat, longitudinal path (20) forming an upper flat surface (54) for holding the substrate to be printed on, the box structures having a plurality of external orifices in their outer face and at least one internal passage in their inner face opposite their outer face. A suction device (6) is able to engage with the internal passages in the box structures circulating over a longitudinal suction region (70) corresponding to at least a part of said flat, longitudinal path (20), so as to produce suction through said external orifices in the box structures circulating over said longitudinal suction region. Inkjet printing machine comprising such a device.