A sheet feeding apparatus for feeding sheets is provided with a multi feed detecting section for detecting multi feed of conveyed sheets in a predetermined detection position of a conveyance path, and first and second discharge sections to which multi-fed sheets with the multi feed detected are discharged, and corresponding to one of a front end position of the multi-fed sheets at the time the multi feed detecting section detects the multi feed of sheets, a sheet storage state of the second discharge section, sheet storage states of the first and second discharge sections, a size of sheets and weighing, selects one of the first and second discharge sections to discharge the multi-fed sheets to the selected discharge section.