The purpose of the present invention is to provide a sheet bundle conveying apparatus capable of discharging a sheet bundle from a processing tray where a binding process is performed toward the downstream side in right posture to a right position. The present invention comprises a sheet bundle conveying apparatus which conveys sheets stacked at a stack portion to a storing portion at the downstream side including a first conveying member which conveys sheets at the stack portion by a predetermined distance, a second conveying member which performs relay conveyance of the sheets conveyed by the first conveying member by the predetermined distance as being set to have a higher moving speed than that of the first conveying member, and a driving portion which drives the first conveying member and the second conveying member.