According to an embodiment, a sheet processing apparatus includes a first tray, a second tray, and a pressing member. The pressing member includes a turning shaft, the turning shaft being located on the downstream side of a transport direction of the sheet to the first tray, relative to an end of the upstream side of the sheet supported in the first tray, and when the sheet is moved from the first tray toward the second tray, rotates about the turning shaft. The pressing member rotates about the turning shaft, to press the sheet toward the second tray at a position on the upstream side relative to the turning shaft.