A sheet stacking apparatus includes a discharge unit, a stacking tray, an acquisition unit, a shift control unit, and an alignment unit. The shift control unit controls a stacking position of a sheet in a sheet width direction in response to shift information acquired by the acquisition unit. The alignment unit aligns a sheet staked on the stacking tray and moves to a position that abuts on a side edge of the sheet in the sheet width direction to align the sheet. The shift control unit controls a stacking position of a second sheet to stack the second sheet on a second position or on a first position depending on where a first sheet is stacked and on shift information of the second sheet.