An apparatus for moving veneer includes a leaf spring having at lower tip end thereof sharpened edges and configured to move a veneer sheet toward its preceding stationary veneer sheet. Further lowering the leaf spring with the tip end already stuck in the veneer sheet causes the leaf spring to be resiliently deformed, which creates a force due to restoring force of the leaf spring that acts on the veneer sheet to move toward the preceding veneer sheet thereby to reduce or eliminate a gap between the two veneer sheets. Additional leaf spring movable with the above leaf spring and configured to hold the preceding veneer sheet during the movement may be provided.