An engine fuel supply system is provided at a reduced cost by using a HC dosing pump that supplies fuel into an exhaust pipe also as a pump for a cylinder fuel supply device. When a signal is generated to command air removal from a cylinder fuel supply passage, the dual-purpose pump is activated, a first on-off valve assumes an open state, and a second on-off valve assumes a close state, so that the fuel is supplied from the dual-purpose pump to the cylinder fuel supply passage via an air-removal fuel supply passage. When a signal is generated to command fuel supply into the exhaust pipe, the dual-purpose pump is activated, the second on-off valve assumes the open state, and the first on-off valve assumes the close state, so that the fuel is supplied from the dual-purpose pump to the exhaust pipe via the exhaust-pipe fuel supply passage.