A fluid supply device, a printing device, and a control method for a fluid supply device can desirably supply a fluid while maintaining good throughput, and can reduce device size and cost with a simple construction. The inkjet printer has an expansion mechanism that enables an ink refill operation in which a movable member expands an ink chamber by moving a piston that moves in contact with a regulator panel disposed to the main device side and supplies ink from an ink cartridge, a comparison means that determines whether or not the amount of ink left in the ink cartridge is less than a specified value, and a CPU that sets a long time mode in which the ink refill operation time is long when the amount of ink left in the ink cartridge is less than the specified value.