A sheet processing apparatus that is capable of aligning sheets in a sheet longitudinal direction with high accuracy when bundling the sheets. A conveyance unit conveys a sheet. A stacking unit stacks a plurality of sheets that are conveyed by the conveyance unit. A grasping member performs a grasping operation that grasps the rear end of the sheet surface of the sheets stacked on the stacking unit. A driving unit moves the grasping member. A control unit controls the driving unit so as to align the sheets stacked on the stacking unit in a sheet conveyance direction by making the grasping member contact the rear end of the stacked sheets after the sheets are stacked on the stacking unit, and controls the driving unit so that the grasping member performs the grasping operation when a following sheet is stacked on the stacked sheets.