In a sheet processing apparatus, which is connected to an image forming apparatus, applies a predetermined process to a plurality of sheets that have undergone image formation as a unit, and has power storage means capable of storing electric power required to execute the process, the output voltage from the power storage means is detected, and when the detected voltage exceeds a predetermined value, the process is controlled to execute the process using the electric power stored in the power storage means in accordance with an instruction from the image forming apparatus. Since the process is executed using the electric power supplied from the power storage means, consumption power can be prevented from temporarily increasing upon execution of the process.