A sheet feeding apparatus comprises a sheet conveying mechanism for conveying sheets along a first conveying path (22) and stacking up them in a sheet stack-feed station (S), a tray (24) for storing a stack of cover sheets (P), a second conveying path (28) communicating with the first conveying path (22), a blow outlet (38) for blowing a jet of air towards the tray (24) to lift up each cover sheet (P), a sucker (30) for sucking the cover sheet (P), a sheet feeding mechanism for conveying the cover sheet (P) received from the sucker (30) along the second conveying path (28) and feeding it to the first conveying path (22), and a pneumatic pump (34) for providing a blow of air and a suction of air. The sheet feeding mechanism is changed to its standby mode when the cover sheet is transferred from the sucker (30) to the sheet feeding mechanism. Upon the sheets having been stacked in the sheet stack-feed station (S), the sheet feeding mechanism transfers the cover sheet. During the standby mode, the pneumatic pump (34) remains inactivated.