To provide a medium stacking device, surely stacking the following medium on the already discharged medium even if it is bent to prevent stacking defect.

This medium stacking device includes: a tray part 3 where sheet-like media 2 discharged from a discharge part 1 are stacked and stored; and a pressing member 4 formed of a sheet body having flexibility, one end of which is driven in rotation at a predetermined timing to press the sheet-like medium 2 discharged into the tray part 3 from above by the rotating tip part.