The invention relates to an ink supply system (2) for an inkjet printer (1) as well as a method of operating the ink supply system and an inkjet printer. The inkjet printer comprises a print head arrangement (6) incorporating several print heads (7) with one or more nozzles (8) for at least one color. The print heads (7) are connected via connecting lines (19) to a supply tank (187) connected via a filling line to an intermediate tank (12) with a conveyor means (16) and a filter arrangement (18) connected in between, and connected separately in each case via second connecting lines (21) to a common return tank (22). Means (32) are provided by means of which a pressure difference can be maintained in the supply tank (17) and/or in the return tank (22) as and when necessary to control a flow of ink from the supply tank (17) via the flow passages (20) of the print heads (7) connected in parallel to the return tank (22). The return tank (22) is directly connected to the supply tank (17) via a return line (24), optionally with a conveyor means (25) connected in between.