In a method and an apparatus for feeding sheets to a sheet-processing machine, the leading edge of the sheet is smoothed before the grippers are closed by further transport into the sheet-processing machine. A curvature or bend in the sheet transport direction is imparted to the sheet. The feed table has, in its feeder region, a curvature in the sheet transport direction, against which curvature the sheet leading edge is laid with the aid of pneumatic or mechanical devices.