A medium-transporting device includes: a medium-support section that has a first mounting surface inclined relative to a horizontal plane; a transport path for transporting a medium; a discharge stacker that is configured to switch between an extended state in which a second mounting surface that is inclined relative to the horizontal plane and that receives the medium discharged along the transport path is formed and a stored state in which the second mounting surface is stored in the medium-transporting device, a control section is configured to perform first control of switching the discharge stacker from the extended state to the stored state after the medium is discharged to the second mounting surface and second control of not switching the discharge stacker from the extended state to the stored state such that the medium remains mounted on the second mounting surface.