A device for stacking veneer sheets (1, 2) while substantially horizontal, the device including a supporting element, that escapes in the advancement direction at a release area from beneath the veneer (2) to be stacked, the supporting element being moved by a conveyor (7), and a controlled element for stopping the veneer to be stacked in a corrected position at a release point. An element for stopping the veneer to be stacked is a gripper (10) that grips the trailing edge of the veneer (2) from below and moves up and down, in the advancement direction of the veneer, and transversely to it, the gripper having a gripping point to the veneer at the trailing edge in the veneer's advancement direction, extended at a distance in the advancement direction from the gripper's transverse travel path.