A sheet processing apparatus which is capable of accurately superimposing or aligning sheets discharged from an image forming apparatus during buffering even when the space intervals between the sheets are reduced. A sheet processing apparatus sequentially receives sheets discharged from an image forming apparatus and carries out post-processing on the sheets. During execution of the post-processing on the sheets, a plurality of sheets are discharged successively from the image forming apparatus and superimposed one upon another around a buffer roller. The conveying speed of the sheets is controlled such that a conveying time period over which a sheet preceding a final one of the sheets to be superimposed one upon another around the buffer roller is conveyed over a predetermined path section is shorter than a conveying time period over which the final one is conveyed over the predetermined path section.